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Any day that John, alone or with Pete, turned up on Julia's doorstep, she was always delighted to indulge him, remarking, "It's lovely to see you. Don't worry about school, don't worry about a thing!" At a time when other parents were making heavy pronouncements about "the future", urging sons to steel themselves for the challenges ahead, John's mother was preaching the polar opposite, and it was music to his ears.

^{Lennon with his aunt Mimi Smith (Photo: Rex)}

Mimi had always maintained a line with John – tough, rock solid and firm. They'd put each other to every test and survived, infuriated but intact. The pubescent John, though, encouraged to skip school by his mother, caused Mimi real grief. Their rows blazed, and with each one he spent less time at Mendips and more at Blomfield Road. A few hours became overnight, then weekends, then a week or more. John was now an adjunct of the Dykins family, and as no one – not their mother, father, John or any of their many relations – told Julia and Jacqui, eight and six, he was not their full brother, they thought he was.

Shotton would also say that John's relationship with Julia was "a source of unending confusion, much as he tried to give the impression of taking it all in his stride". There were moments of emotional turmoil for a strongly sexual teenage boy in the company of a woman who had a history of liberality uncommon in her time, a woman aware of her effect on men, a woman he knew to be his mother but didn't always act like it. As he'd recall in a personal audio diary in 1979:

"I was just remembering the time when I had my hand on my mother's tit. It's when I was about 14. Took a day off school. I was always doing that, and hanging out in her house. And we were lying on the bed and I was thinking, 'I wonder if I should do anything else?' And it was a strange moment, 'cause I actually had the hots for some rather lower-class female who lived on the opposite side of the road. But I always think I should have done it, presuming she would have allowed it."

In 1956, with the coincidental arrival of both rock and skiffle in the lives of young British boys, John became obsessed with the guitar. He didn't have one, but Julia taught him to play banjo. The first song she showed him was Ain't That a Shame, not Fats Domino's original recording but a safe white cover version by Pat Boone, the one she knew from the radio. John would call it "the first song I was able to accompany myself on", those words relating a vital dimension to Julia's teaching: without the harmonica, John was free to sing along with the chords his fingers were forming. And he could really sing; his was a voice that came naturally and honestly. His hands-on musical education also had balance. Julia showed him how to play at least four sweet songs from her youth: Don't Blame me (1933), Little White Lies (1930), Ramona and Girl of my Dreams (both 1927). All would remain lifelong favourites… but it was rock and skiffle that dominated John's mind, to the point where he formed his own group, the Quarry Men, with boys mostly from school.

The Quarry Men were one of scores of skiffle groups suddenly strumming and plucking away in every suburb of Liverpool. They didn't rehearse at Mimi's house because she emphatically didn't want the place full of kids, and also had to consider her lodgers, Liverpool University students who needed peace and quiet – but the lads were warmly welcomed by Julia. Sessions often took place in the Dykins's none-too-spacious bathroom, John needing to hear his voice bounce off the shiny tiles, approximating the slap echo sound Sam Phillips had given Elvis Presley and Carl Perkins at Sun Studio, Memphis.

Julia also bought John his first guitar. With the skiffle boom temporarily stripping them from shops, retailers had to source them with cunning. John's was a South African-made instrument bought from a south London mail-order firm advertising in the popular lowbrow weekly Reveille. The ad appeared in the issue of March 7 1957:

ROCK 'N ROLL GUITARS, REAL PROFESSIONAL, SENT FOR 20/-

That was enough to grab the eye, but the small print uncovered the real cost: it was £1 down and then 21 fortnightly payments of 20s 3d, for a total of £22 5s; or one instant payment of 19 guineas plus 5s carriage, total £20 4s. This was expensive. John (who always remembered it costing £10) later said it was bought "on the never-never", which must mean Julia was committing to a shade over £1 from Bobby Dykins's wage-packet every two weeks all the way to the start of 1958 – a period during which John left Quarry Bank and enrolled at Liverpool College of Art.

^{The Quarrymen perform at The Casbah, Liverpool on August 29, 1959 (Photo: Michael Ochs Archives)}

In the final weeks of 1957, with Julia in mind, John wrote his third song. The first, Calypso Rock, was written in the spring, when West Indian sounds were being pushed by record companies as "the next big craze", superseding rock, which surely couldn't last much longer. Among the songs Julia liked to sing around Blomfield Road was the 1939 dance-band and film number Scatterbrain, and John was fascinated by the rhythmic flow of such lines as "When you smile it's so delightful/ When you talk it's so insane/ Still it's charming chatter, scatterbrain." John sat with his guitar and started playing around with chords and phrases in the style of new American hero Buddy Holly, and a new song began to emerge, words and music.

He called it Hello Little Girl, and though it's nothing like Scatterbrain, this was its spring. The earliest known and surviving recording of Hello Little Girl is from 1960, and the Holly influence is overwhelming. For an early attempt at songwriting, it's a remarkably catchy tune, appealing and direct. The words are written in the first person: he's besotted with a girl but she never seems to see him standing there, he sends her flowers but she doesn't care, but still he hopes there'll come a day when she'll think of him and "love, love, love". And this time, having been unable to hang on to his earlier attempts, John found a way of remembering it, going over Hello Little Girl phrase by phrase until it was embedded in his head.

By this time, John had yet another friend. In July 1957 he'd met Paul McCartney, who lived in nearby Allerton and was close to two years his junior. Like all John's other pals before him, Paul fell in love with Julia from the outset, finding her more like a big sister than a friend's mum. "I always thought she was a very beautiful lady, with long red hair. I know John absolutely adored her: one, on the level that she was his mum, but also because she was a very beautiful woman and a very spirited woman. She was very lively." Paul thought it was fabulous that she played banjo, finding her "great, gorgeous and funny". While observing John's awkward relationship with Twitchy, Paul could see how much he loved his mother – John "idol-worshipped her", and when they left the house "there was always a tinge of sadness" about him.

As an alcoholic with a restaurant job in the city, Bobby Dykins had been courting trouble for years, driving home to the southern suburbs in the early hours. Just after midnight on Friday June 20 1958, however, half an hour into Saturday morning, his luck ran out. He was driving drunk along Menlove Avenue, just beyond Mendips, when he was observed by a constable walking his beat. Though the car was going at normal speed, its engine was racing. Dykins should have turned right at the lights but, seeing the policeman, shot left, and the car mounted the reservation between Menlove Avenue and Vale Road. The constable got to the road and flashed a torch, signalling him to stop, but Dykins drove on and came to a halt further along Vale Road. Noticing that the driver's breath smelled strongly of drink, and that his speech was slurred, the policeman asked him to get out; Dykins opened the door and fell out, and had to be helped to his feet. Told he was being arrested, Dykins became aggressive and abusive, shouting, "You ------- fool, you can't do this to me, I'm the press!"

Dykins was taken to Woolton police station where a doctor certified him unfit to drive. Held overnight in a cell, he was charged in the morning and taken straight to the court, to be remanded on bail of £5. When he reappeared there on July 1, his solicitor entered a guilty plea and Dykins was fined £25 plus costs, had his licence endorsed, and was disqualified from driving for a year. The incident was reported in both of the city evening papers and also twice in the local Liverpool Weekly News, which will have caused no little embarrassment to the family. Julia's four sisters didn't think very highly of her man-friend.

Dykins immediately left or lost his job: either he was dismissed or gave it up, incapable of getting home late from the city, taxis unaffordable. The drink-driving incident had set in motion a sequence of events that reached a terrible calamity two weeks later.

Julia was often at Mimi's. Their original relationship had been rekindled since John began shuttling between them. Her visit on Tuesday July 15 had a purpose, though. The summer term at Liverpool College of Art had ended on Friday July 4, three days after Dykins lost his licence and his job and had been fined the equivalent of about three weeks' wages, cash they may not have had. Financially, things were suddenly tight at Blomfield Road, and Dykins had told Julia a stark truth as he saw it: they could no longer afford to have John staying at the house. It was going to be hard enough to feed the two girls without a gluttonous young man eating them out of house and home. If Julia didn't agree, then perhaps discussions became heated, because – heavy-hearted or otherwise – she ended up going to Mendips to convey this very message. John was at Blomfield Road when she paid the visit.

Having said what she'd gone there to say, Julia left for home at 9.45pm. She had three choices: to walk all the way, perhaps cutting across Allerton golf course; to walk down to Woolton Road and catch the bus to Garston (and then walk); or to cross Menlove Avenue and catch the bus going north, towards Penny Lane, and then change for a bus cutting back south again, to Springwood. She chose the last. On another day, Bobby might have come to collect her… if right here on Menlove Avenue he hadn't lost his licence… but for which she might not have been here at all.

Mimi sometimes walked Julia to the bus stop, but this summer's evening they parted at the gate. A number four bus was due within a couple of minutes. Just as Julia was about to head off, John's friend Nigel Walley came along, hoping to find John at home.

Mimi said he was out, then Julia said, "Oh Nigel, you've just arrived in time to escort me to the bus stop." As Nigel explains: "Julia said her goodbyes to Mimi and I started walking with her. When we got to Vale Road I turned up while she crossed Menlove Avenue, and at that moment I heard a car skidding and a thump and I turned to see her body flying through the air. I rushed over. It wasn't a gory mess but she must have had severe internal injuries. To my mind, she'd been killed instantly. I can still see her gingery hair fluttering in the breeze, blowing across her face."

Walley ran to Mendips but the commotion had already brought Mimi back outside. By chance, long-term student lodger Michael Fishwick was there too. "Mimi and I heard the screech of brakes. We looked at each other and took off in full-flight out of the house. We ran up the road and across and there was Julia, looking quite peaceful, bloodied only at the back of her head. A crowd gathered. Someone ran off to ring for an ambulance. She gave one final breath and died."

Mimi, still in her carpet slippers, went in the back of the ambulance that sped Julia's body to Sefton General Hospital. What hell that must have been. Fishwick followed with her shoes and handbag, and then the police took them to Blomfield Road where no one yet had any idea of the terrible events. Mimi would recall John being out at the time, but when he came in and was told the news he broke down, saying, "Oh God, oh God." John's own recollection, when talking about it nine years later, was different. He remembered a policeman coming to the door and, as if in a film scene, asking for confirmation he was Julia's son. When John mumbled a yes, the constable replied, "I'm sorry to tell you your mother's dead." Bobby phoned for a taxi to get the two of them to the hospital. As John would recall, "He [Twitchy] said, 'Who's going to look after the kids?' and I hated him. Bloody selfishness."

John gabbled hysterically all the way, but when they got to the hospital, unlike Bobby, he couldn't bring himself to see the body. "It was the worst thing that ever happened to me. We'd caught up so much, me and Julia, in just a few years. We could communicate. We got on. She was great. I thought, F--- it, f--- it, f--- it. That's really f----- everything. I've no responsibilities to anyone now."

The funeral was the following Monday, July 21, at Allerton Cemetery. John never spoke of it publicly and there's only one reliable witness to confirm he was in some way part of it. His cousin Liela (while not saying explicitly that John was or wasn't at the cemetery) would relate how she and John sat and ate some post-funeral sandwiches. "John and I just sat there on the couch, him with his head on my lap. I never said a word. I can't even recall telling him I was sorry. There was nothing you could say. We were both numb with anguish."

^{Julia's death made John Lennon more embittered, cynical, edgy and volatile (Keystone Pictures USA / Alamy)}

The fatal accident hardened, irrevocably, Lennon's view of the Establishment, and especially the police. Coming to believe the driver who killed his mother was "a drunk off-duty cop", his respect for authority, and especially the law, crumbled and would only ever worsen. Where most people saw law and order, John would only see rank hypocrisy. The driver, Eric Clague, was indeed an off-duty cop; he was also a learner-driver and shouldn't have been on the road unaccompanied, and was suspended from the force because of it; but he was never charged with being drunk, and alcohol wasn't mentioned at the inquest. Though it's possible it was suppressed, it's also possible this cornerstone of John's lasting grudge against the police was set in misinformation.

The grief was not John's alone. In one instant, four children lost a mother, an estranged husband lost a wife, a man lost his partner, four women lost a loved sister, three nephews and a niece lost an aunt and Liverpool lost one of its colourful characters. The fallout was widespread.

For John, who'd grown up without Julia from the age of five, losing her again at 17, with such appalling finality, was the most tremendous and irreconcilable heartbreak. As he would put it, with customary deafening economy, she had him but he never had her. He became more embittered, more cynical, more harsh, more uncompromising, more edgy, more volatile than ever. As he would recall in 1980:

"[It] was really a hard time for me and it just absolutely made me very, very bitter. The underlying chip on my shoulder I'd had as a youth was really big then. Being a teenager, and rock and roll and sideboards and art school and mother being killed just when I was re-establishing a relationship with her – it was very traumatic for me."

After this, his behaviour seemed worse by degrees, and John became the definitively gifted yet troubled young man, the mixture that defined him: artistic and sarcastic, literate and cruel, brutal and tender, swift and funny, contemptuous of all pretence.

Extracted from The Beatles – All These Years to be published by Little, Brown on Oct 10 at £30. To order for £26 plus £1.35 p&p call Telegraph Books on 0844 871 1515 or visit books.telegraph.co.uk.

Copyright © Mark Lewisohn 2013