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In Make Me A German, a BBC programme broadcast next week, the Rowlatt family discovers – as we did – that life in Germany might look similar from the outside, but is very different on the inside. The premise of the programme is that Justin Rowlatt, a journalist, and his wife Bee take up the lives of an ordinary German family to experience their robust economy, superior quality of living and legendary efficiency. Justin works in a pencil factory, one of the small enterprises that employ a majority of German workers, while Bee stays at home to look after the children. Justin is impressed by his German colleagues' dedication, while Bee is delighted by a German "forest kindergarten" where children climb trees and toddle around dragging branches – although she is dismayed by the four-hour daily quota of housework she is expected to fulfil.

Still, the programme is destined to get viewers wondering what us Brits could, perhaps, learn from the Germans.

Just over 98,000 Britons live in Germany, around a third of them British soldiers and their families. Berlin has a particularly strong pull for artists – Turner Prize winners Douglas Gordon and Susan Phillipz live here, as does Tacita Dean. The German capital's appeal combines history, generous cultural subsidy, and – until rents started to rise recently – cheap spaces to live and work. The city's attraction to laid-back, creative types is further enhanced by the fact that you rarely see a suit here; the bankers are all in Frankfurt.

One of the most appealing aspects of German life is the renting culture. Traditionally, tenants have enjoyed secure and affordable accommodation and felt able to treat a rental flat as a home. It's not quite true that all Germans rent. In fact, over half own their own homes. The big difference is that the housing market here has traditionally been slow-moving. Unlike other countries with credit-fuelled housing rollercoasters, few Germans have reason to see their property as their main investment.

My wife and I found more surprises in store at the bank. We were greeted with old-fashioned courtesy by a bank manager who escorted us to a private room and guided us through our account options over coffee and fizzy mineral water. He asked us if we wanted a credit card before pointing out quickly: "We don't offer them."

The bank manager sounded almost wistful as he added: "The bank did offer them, but customers didn't want them."

The German word for debt, Schuld, also means guilt. Germans are profoundly attached to paying in cash. In shops, customers will often count out the precise amount, down to the last copper. Around half of Germany's property owners own their homes outright, with no mortgage or outstanding loan. In Swabia, Germany's prosperous south-western corner, the saying goes: "Schaffe, schaffe, Häusle baue" – literally, "work, work – and build a little house."

Germans can't resist a touch of smugness about this, ignoring the role of their banks in fuelling the credit boom. In 2008, Angela Merkel offered this analysis of the financial crisis: "You just have to ask the Swabian housewife. She would have given us some worldly wisdom. You cannot live permanently beyond your means."

The parsimony extends to industrial relations, where workers have accepted years of wage restraint. Indeed, a desire for consensus underpins the German business model, which emphasises harmonious relations between unions and employers – unlike the more free-wheeling Anglo-Saxon system. As youth unemployment soars across Europe, Germany's excellent apprenticeship system attracts many jealous glances. In 2010, Siemens struck a deal with its 128,000-strong German workforce to guarantee their jobs for life, while plenty of other firms provide similar guarantees for shorter terms. Many companies reduce employees' working time rather than laying them off. Despite the crisis in its European export markets, Germany's unemployment rate, of 5.3%, is the lowest in Europe.

In Britain, childcare costs swallowed a huge chunk of our salaries. Here, our daughter attends a state-run nursery for which we pay a contribution of 48 euros a month. She attends five days a week, spending hours outdoors in their sandy yard. In London, a nursery place cost us £600 a month for three days a week. Meanwhile, our son attends a state-funded school with an excellent reputation that offers a bilingual education in English and German.

But life isn't entirely rosy for mothers. In Germany, working mothers are described as Rabenmütter – "raven mothers", from a Biblical verse which says that ravens neglect their young. Many schools here close at lunchtime, a system built on the presumption that mothers will stay at home. The first time I took my daughter to nursery, I was asked if I was a single father.

Indeed, one of our first culture clashes was over our children. "There's now a ruling that children's noise is acceptable," we were told by an expat friend, pregnant with her first baby, soon after we arrived. She was referring to a change in the law three years ago, which protected children's right to be noisy.

It seemed the news hadn't filtered through to our apartment block. Not long after we moved in there was a knock at the door, and one of our downstairs neighbours asked, with a pained expression: "Are your children roller-skating?" They weren't. It was the sound of our three-year-old daughter, Nila, rattling a toy pram over the bare floorboards.

Another of our neighbours texted me to ask that our children stop bouncing a ball indoors. Unlike the Rowlatts in Make Me A German, we haven't had a police officer call to deliver a rebuke about the noise of children playing. But just in case, both ball and pram are now tucked away in a store cupboard.

The attitude towards children hasn't been the only eye-opener. After experiencing its slick trains and chic hotels on holidays, we had high expectations of German efficiency. But compared with Britain and the US, customer service in Germany can be dismal. It took three months to get connected to the internet, a lifetime when you're a journalist. After one internet provider lost our forms, then missed two appointments, my wife Meera walked into a rival firm and refused to leave until they guaranteed to connect us. I'd assumed Germany would be more efficient,I grumbled to our Swedish neighbour. "Nein," he replied cheerfully. "Deutschland ist bürokratisch".

Germany is a society driven by rules that often serve to enhance communal life at the expense of individual freedom; the restriction on Sunday trading, for example, makes Saturday mornings a whirl of last-minute grocery shopping while enforcing rest on the Sabbath.

Another, more serious, problem is the attitude towards immigration. There are few non-white faces in positions of authority, perhaps because Germany's least ambitious schools act as a dumping ground for ethnic minority children. Turks form the largest ethnic minority group. Many came over in the 1960s when the demand for labour was high, fuelled by the construction of the Berlin Wall in 1961 that restricted movement within the country. Theirs is an often uneasy relationship. For years, German police failed to stop a neo-Nazi gang that murdered Turkish businessmen, preferring to blame the killings on foreign gangsters. Germany often seems more comfortable engaged in introspection over the absence of the Jews, than it is dealing with the presence of the Turks.

Until very recently, German law gave citizenship to anyone of German descent – under the jus sanguinis "the right of blood" – while denying it to Turkish children born in Germany. Now the law requires children of foreign parents to choose one nationality before they turn 23. A notion of insiders and outsiders seems embedded in a language that divides the world into Deutschland and Ausland.

For me, though, a big part of the appeal is that Berlin is young. It is just 24 years since the Wall came down, and 14 years since the German parliament moved to the Reichstag building. Cranes remain busy above the once-divided city.

Berlin is fast becoming a hub for technology firms. In my first few weeks here, I rented a desk in a shared office space. My neighbours were a host of digital start-ups, and each day I would come in to find a new sign tacked up on a wall or an old one in the bin, as a baby firm moved on to greater things or was consigned to oblivion. Berlin feels like a city on the move.

We hope to stay for at least two years, giving the children a chance to learn the language while we all learn more about the country at the very heart of Europe. There is much to admire about Germany: I am struck by the quality of the childcare, the relish with which Germans enjoy their beautiful countryside, the freshness and seasonal rhythm of German food, and the success of their manufacturing industry.

By comparison, Britain often seems a more fragmented society, though it is perhaps one with greater individual freedom.

Make Me A German is on BBC2 at 9pm on August 6