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A stream of albums (with breaks for babies) followed, with dwindling success. Then last year she fully re-entered the public consciousness by competing on Strictly Come Dancing. Fans were devastated when she was kicked out – she came fourth – before having a chance to repeat the Charleston described by judge Darcey Bussell as "just perfect". Was she? "Nah," she laughs. "What if I screwed it up? It was much better to leave it as good as when it happened – anyway, if you want to see it, it's on YouTube."

An album, Wanderlust, followed and reached No 4 in the charts – her first time in the top 10 since 2007. Its success was well deserved: the poppy dance that made her name is gone, replaced by haunting, reflective ballads – in Ellis-Bextor's words, "a mix of Eastern European and folk and very British". Realistically, however, the Strictly effect must have given it a sales boost.

"Well, yes and no," Ellis-Bextor shrugs. "Strictly is very much its own world. I don't think necessarily people think: 'I loved her waltz, I'm going to listen to her songs.' I could have been rubbish, I could have been voted out in the first week. I don't think you should ever do anything in the hope it will sell something else, particularly something as intense as Strictly. If you don't want to learn how to dance, then don't bother."

In fact, it was Ellis-Bextor's rock-solid home life (a tattoo on her right arm reads "Family") that gave her the confidence to push her career to new heights.

"Strictly had been asking me on for years, and I'd always said no because I make dance music and I was worried what people would think when they found out I couldn't dance. I'd never had a lesson in my life. But last year, I thought: 'Sod it.' I'm 35, I've got three children, I've got my husband, I'm happy, life is good. I don't mind what people think of me. I'm already a mum who embarrasses her kids – I might as well own it."

The album's quirkiness "came from the same part of my head. In the world of the major record labels, you're encouraged to think there are certain things you've got to do, but I funded this myself; it was totally my own thing. I'd much rather indulge myself with this than with a sports car."

She chortles. "If you're trying to make some money, there are easier ways to do it than make a whimsical record about Eastern Europe, but people aren't daft and ultimately they want something with a bit of soul and authenticity."

Ellis-Bextor has always been a study in unconventional conventionality. Her father is TV producer Robin Bextor, her mother (her parents divorced when she was four) former Blue Peter presenter Janet Ellis, who scandalised the nation by having Ellis-Bextor's younger brother Jackson out of wedlock.

She attended the pukka all-girls Godolphin & Latymer school. But rather than go to university, she became the singer in the band Theaudience. "I literally took the bus to the record company after my last A-level and signed the contract. I could see some of my friends' parents thinking: 'What?' I really appreciate how cool Mum and Dad were about it."

Her parents were equally supportive when, aged 24, she became pregnant after only six weeks with Richard Jones, then her boyfriend, now her husband, bassist with the band the Feeling. She developed pre-eclampsia, meaning Sonny was born two months early by emergency caesarean. "That wasn't ideal, but it was all caught up in the strange drama of it all: you meet someone, you fall in love, you find out you're having a baby, then, by the time you've been going out for only nine months, you have the baby."

She also had pre-eclampsia with Kit, now five, who had to be delivered at 32 weeks, weighing just 2lb 6oz. Only her third pregnancy, with Ray, now two, went to term. "Until then, I hadn't realised how much we'd missed out with the other two. It was just so much easier when you have your baby with you from the offset and they're big and they come home with you and they feed."

Now she's toying with the idea of a fourth. "But on holiday there were a couple of other families with four and they looked really harassed. Most of my friends started having babies around the time Ray was born, so I'll see how I feel when they start having their second ones. I might think: 'Ooh that looks nice', or I might think: 'No, I'm fine thanks!'"

For now, she's busy promoting her latest single, The Deer & The Wolf, and performing all over the world. She has an especially ardent Russian fan base, perhaps no bad thing since, as pop star Lily Allen recently complained, the only way to make money as a musician today is if "some rich kid in Russia" asks her to sing at their birthday party.

Ellis-Bextor shrugs. "If anyone wants me to do their birthday party, great. You can't be snobby, I'm an entertainer, that's what I do. If someone loves what you do enough to want you to sing at their party, that's quite a compliment."

Again, the practical attitude seems at odds with her ethereal appearance, but Ellis-Bextor says: "I'm very gung-ho."

On Wanderlust, she unveils a stunning voice. The early monotone singing style, she says cheerfully, was "just to make me feel a bit more like I have control over something I have no control over, to protect my sense of self".

She adds: "When I started, I sort of saw the whole business as like a really long, drawn-out dating process. I thought: 'I still want to have things in 10 years I can reveal to people, and if the business spits me out after two years, I don't want to feel I played all my tricks and it wasn't enough.' You don't have to smile when you sing the first couple of songs. As it grows, then maybe you can show you're having a nice time."

She's showing that now, relishing an existence where one day she's accompanying Sonny's class on a school trip and the next taking a private jet to DJ in Azerbaijan. "It's definitely not a real job, but I love the craziness of it," she smiles. "When you have your family none of it really matters. If someone's giving you hassle, you just think: 'Who cares? I'll go and build a marble run.'"

Sophie Ellis-Bextor's new single, 'The Deer & The Wolf', is out on September 1