The English – not the British, as the Scots, with their love of tenements, think differently – have firm views when it comes to living up high. It’s fine for singles and couples, apparently, but the received wisdom is that it’s positively inhumane for families with young children. Once you breed, you are expected to find a suburban house with a garden. So what about this one, then – a six-bedroom house, designed for a young family, with plenty of outdoor space, that is perched on top of an old warehouse in the heart of the capital?

Given that it is on the fringes of the financial district – it’s on Clere Street, in the Old Street/ Shoreditch enclave – you would expect it to be the eyrie of an investment banker with an unusual attachment to family life. Not a bit of it. It’s the self-built home of part of the Richard Rogers design dynasty, and he helped to create it.

This, then, is where you will find Zad Rogers, 43, television producer and son of the famous architect, with his wife, Lucy Musgrave, 41, architecture and landscape consultant, and their four daughters, aged 11, 9, 7 and 5. Zad, in case you were wondering, is short for Zadoc.

They are no strangers to living at altitude – before they built this place, the family lived considerably higher, in a large flat in one of the Barbican towers. As the children continued to arrive, however, they needed more space – the old story. Here is where most people go down the suburban route, but Musgrave and Rogers had other ideas. As one of Zad’s producer roles was on the property series Location, Location, Location, they were almost bound to.

They had a friend who owned the warehouse, which had a flat roof. The idea of a rooftop extension was mooted. A long and complicated process ensued, centred on the legal concept of roof rights and air rights – different things, apparently, in this case involving the block’s respective leaseholder and freeholder, as well as endless negotiations, stop and start. The block beneath them changed hands. Another one was built next door. Finally, they got to build.

The main architects are an award-winning couple, Mike Tonkin and Anna Liu. At one point in the process, when the costs seemed prohibitive, Zad’s dad stepped in – Richard Rogers took on the project as developer to help out his family. A firm believer in high-den-sity and sustainable city living, he was also putting his money where his mouth was.

Conjuring a desirable family home out of thin air, making space where there appeared to be none, contrasting new with old – you could say this was a manifesto statement. So, Rogers encouraged Tonkin and Liu, and the house design became more ambitious. A lot taller, for a start. The top floor seems twice as tall as normal. You notice it in the bathroom, in particular, where the shower head, just for a laugh, is placed way up near the glass ceiling and seems miles away.

Eventually. Zad and Lucy took the project back themselves and finished it. The whole process started back in 2001, and the family moved in only in August 2006. And now – well, working on such projects is clearly in the blood. They want to build another home, somewhere else – as yet undecided. So they are seeing if, despite the turmoil taking place close by in the City, and the paralysis in the housing market, they can buck the trend and find a buyer who wants a unique home. This attitude, I think, is described as counter-cyclical. The guide price is £2.5m.

The first thing to say is that this is not a flat. It is a complete two-storey house with a roof terrace. Inside, it covers 2,330 sq ft. You could put it down on the ground, surrounded by gardens, and you would not think it strange. Although, in that case, you might well put the living areas on the lower floor and the childrens’ bedrooms above. Here, it’s the other way round, so as to make the most of the city views. And there are two ways to get from one level to the other, as it has inside and outside staircases.

There’s nothing any child likes more than a house with two sets of stairs, and so it proves. “The children and their friends spend all the time dashing up and down round the circuit,” Lucy says.

The four of them are all safely out of the way at school the day I visit. We stare out across the rooftops at the curious mix of old warehouses, some of them still in semi-industrial use, and new skyscrapers. “It’s a nice urban view,” Zad says with satisfaction. “And there are some good schools here for the children.”

In fact, they walk to school, which somewhat gives the lie to the idea that only the child-less and the old inhabit the real centre of London. There’s quite a population round here these days, and the nearby primary school is brand-new. You also have one of the world’s leading arts centres nearby, in the form of the recently spruced-up Barbican, and as many trendy bars as you can shake a cocktail at.

When the children aren’t using the house as a race circuit, they’re in “the Pit”. Whereas the lofty upper floor of the house – which contains the master bedroom and bathroom, as well as the kitchen and living areas – exploits its position with stonk-ingly huge glass walls, made out of energy-efficient glazing panels, the lower floor has the equivalent of a cave in it. The children’s bedrooms are arranged along one side, opening onto a broad balcony. This leaves space for the television/ cinema room. Everyone dives into the sunken seating area – the Pit – which is filled with bright-green cushions. Telly and movies are delivered through an overhead projector.

The point about the way the house was built, Lucy says, is that the rooms can be arranged any way you like. “Each floor is a clear space, with no columns,” she explains. “We decided we’d spend the money on the main structure, so it can be adapted however people want. If a buyer doesn’t want all those bedrooms, you can take down the walls between them.”

Thus, the floorplan is almost childishly simple, given excitement by such touches as the entrance via a gantry from the next-door building and the slightly vertigo-inducing external staircases – one of them a spiral winding up to the roof.

The finishes are relatively basic. The couple choose instead to highlight their fine old pieces of well-worn furniture, many inherited from Richard Rogers’s mother, Dada, for whom he created a house in Wimbledon back in the 1960s. The metal-mesh balconies are intended to be colonised by climbing plants, a process that is well under way.

One thing they won’t divulge is how much it all cost to build – “a lot of money” is all Lucy will say. This was expensive building, all right, involving closing surrounding streets to bring in cranes to lift the beefy girders and weighty glazed units into the sky, and erecting a hoist for the other materials. There was no other way. So I’m not surprised that it looks as if the money ran out when it came to the roof terrace. Up here, you could surely create a magical roof garden, and there are 360-degree views around the City – but it’s just a bit of decking with a mossy patch at one side. There’s a project for someone.

That aside, it’s hard to fault this family house sitting on the London skyline. It’s a romantic vision of how a future city might be, and it proves that you don’t have to sacrifice quality of life when you grow up and have children. In fact, because it’s designed in such a way that it’s just about impossible to fall off, and is way up out of reach of any ne’er-do-wells, you could argue that it’s the most secure environment possible in which to bring up a family.

And, let’s face it, it’s just the best place for children to show off to their friends.

Zad Rogers and Lucy Musgrave’s rooftop house on Clere Street, London EC2, is for sale through The Modern House; 0845 634 4068, www.themodernhouse.net

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