There is something very English about building a magnificent house that nobody can see from the outside. It is the opposite of ostentatious display. It also taps into our wider fascination with secret spaces, the lairs of superheroes and villains. The entry to the spy headquarters in The Man from Uncle was through a dry-cleaning shop, wasn’t it? All these are really just versions of Narnia: magic places where only the chosen few can go.

Now, if you have a spare £5.75m, you can buy what could be the best house of this type ever.

It is big — 6,000sq ft, in fact, 135ft long by 42ft wide, with a floor-to-ceiling height of 16ft in its cavernous living space. It is close to the heart of London, but you would not know it. The house is in a cobbled mews reached through an arch, but even if you find the mews, its presence is still not obvious. There are a couple of modern shop fronts among the ramshackle old ones. One is the entrance to offices. The other? Press the button on a discreet device and it slides into the air, revealing a courtyard where you can park your Maserati. Or your lightweight bike. Because although you are about to enter a multi-millionaire’s pad, complete with suspended glass swimming pool and a million electronic gizmos, this is all very ecofriendly.

You may not have heard of architect Richard Paxton. He died — suddenly, aged 49, as the result of a heart condition — in March. He designed this house for himself and his family off Regent’s Park Road in Primrose Hill, north London. Although he won awards for the new Soho Theatre and the multi-arts Jerwood Space on the South Bank, houses were Paxton’s passion.

He designed the homes of many a famous name — Douglas Adams, Griff Rhys Jones and Anna Ford among them. But he constantly, restlessly, designed new homes for his family, too. Usually in places too difficult for other developers to touch.

The Paxton House, as it is now known, is typical of his approach. It is on the site of a former garage, surrounded by high walls that make conventional windows impossible. Always a man to take a risk, Paxton bought the site in 2001 without planning permission after various developers had failed to make it work. He solved the problem in high style by slinging something vaguely resembling Thunderbird 2 into the space, putting offices underneath to help pay for it, and then crafting the ultimate family and party home inside.

Who needs windows when you have giant curving glazed roof sections that slide open at the touch of a button? The family — Paxton, his artist/architect wife Heidi Locher and their children Caitlin, 18, and Freddie, 16 — moved into the house in 2003, but — because of pressure of work elsewhere — it was never quite finished during Paxton’s lifetime. Since his death, Locher and members of Paxton’s architecture firm have completed it for sale. Why? Because the family is on the move again, this time to nearby Hampstead, where the last of Paxton’s extraordinary series of homes is nearing completion.

“We adore the buzz of projects,” says Locher, who remain in awe of her late husband’s skills. “I keep finding these clever things,” she says, “and I think, ‘It worked. He pulled it off’.”

The final home in the series, now being built in Hampstead, is clearly influenced by its predecessor, with a similar opening roof arrangement. As it is has to be unobtrusive, the Oval House will be sunk into planted earth banks. Paxton called it “a doughnut in the city”. It began life as a project for a client, but when he withdrew, Paxton, typically, took it over for himself.

I met Paxton a few times, and his enthusiasm for his craft was extraordinary. He thought of absolutely everything, right down to the tiniest detail. At his previous home in Clerkenwell Green, he made shimmering balcony-fronts out of the fine mesh normally found in cafetieres.

The Primrose Hill house has dozens of clever touches like that. They start at the entrance, where you walk in from the yard and look up. Restful, refracted daylight washes down. It reaches you through the glass swimming pool hovering off to one side above you.

A shallow ramped staircase takes you up alongside the pool to the main living area. But you don’t have to walk. The bottom landing has a minimalist handrail on it. Press a button, and this section of stone floor rises up to become a miniature funicular railway, trundling you and your cases of wine up to the top.

To describe all the ingenious electronic features of the place would take far too long: it’s enough to say that the house is divided into three zones: parents’ bedroom and bathroom zone at one end, vast living/dining space and swimming pool in the middle, and children’s/guest area at the other end. A glass bridge links both ends to each other at the upper level.

Each zone has a handset that controls everything from audio and television to lighting and the opening of the front door and roof. You don’t have to worry about being flooded by a sudden storm when you are out: the roof sections are fitted with rain sensors, and close themselves.

But what attracts me far more are the non-electronic things. Locher sits down at the table in front of the island kitchen (typically, it is linked via double-ended drawers through to an enclosed kitchen behind so you can send dirty dishes through and get fresh food back as if by magic). She slides back a section of the island’s stone frontage to reveal a fridge full of bottles.

“Richard loved this. He would sit here at parties giggling at people’s reactions when he revealed the bottles,” Locher says. Similarly, in the bathrooms, adjustable mirrors allow you to see the back of your own head.

“That was the thing about Richard,” she says. “He had a grasp both of the big picture and of the fine detail. It’s a very serious project, done with a light touch. His ambition here was to design the most beautiful house you could imagine — but very smart and ecofriendly.”

The big picture includes the house’s energy strategy: Paxton installed a system of heat recycling that uses the building’s foundations to transfer surplus heat into the ground in the summer, to be reused in the winter. The house’s fuel bills — and carbon emissions — will be remarkably low as a consequence.

The house could have six bedrooms — though, at the moment, one is arranged as a gym/screening room and one as Locher’s studio. Three of the bedrooms are on two levels — bed above, living space below. The master bedroom has two bathrooms, a dressing room and a study beneath it. As well as the swimming pool, there is a zen-like shallow pool in the living area with water gently trickling into it. An enclosed corridor at the western bedroom end is fitted out as a library.

The house is so ingeniously arranged, and plays with light so masterfully, that you don’t mind that it is almost completely landlocked. It doesn’t need a garden since the living area opens up to the sky. Anyway, Paxton saw the house as the escape zone.

“It’s that thing about the secret garden — the door in the wall with some amazing place behind it,” says Locher. Paxton managed, however, to engineer a patch of outdoor space where the site widens out at one end. So three of the bedrooms have access to an outdoor terrace. Nothing so conventional as a door, of course: in two of them, curved glazed walls rotate upwards to let you out.

For all his confidence, skill and bonhomie, Paxton was a surprisingly modest man. He won competitions for projects but never marketed himself. Even so, his reputation grew steadily by word of mouth. Rightly so. This house is like no other. It is the work of a master.

The Paxton House is for sale with Knight Frank, 020 7586 2777, www.knightfrank.co.uk; Goldschmidt & Howland, 020 7289 6666; www.g-h.co.uk; and TK International, 020 7794 8700, www.t-k.co.uk

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