Eglon House landed like a tasteful modernist spaceship on a mews in London's Primrose Hill sometime towards the end of 2015. The response, mainly, was bemusement. The site had previously been a shell-casing factory during WWI, a dairy for the cattle that grazed on the local fields, and latterly a museum and a recording studio where Ultravox made "Vienna". In its latest incarnation, the land has been developed into two distinct buildings set around a cobbled courtyard: an Art Deco five-bedroom townhouse; and a double-height, museum-grade art gallery. It's a live-work lair for the family-oriented Bond villain. The sections are connected by a subterranean floor that has this bizarre property's most fantastical feature. With a whir and a whoosh, the floor sinks from beneath your feet, fills with water and becomes a swimming pool. At one end is a three-metre-wide cinema screen — waterproof, naturally — one of the largest, HD LED displays ever made.

No one entirely knew what to make of Eglon House. At 13,154sq ft, it is practically the size of an aircraft hangar. Your neighbour on one side will be the Al-Fayed family; on the other are council tenants, who hang washing outside their front doors. After it was put on the market in December 2015, The Daily Telegraph asked: "Is it a home, an office, a work of art or a tax wheeze?"

A spokesperson for Savills, the upmarket estate agent instructed to sell Eglon House, outlined who they thought would be interested: "The successful buyer will no doubt be globally nomadic with multiple homes in America and elsewhere in Europe, spending time in key cities around the world." Early on, there were murmurs that an art foundation and a famous musician were seriously considering it. Oh, yes, the price: £24m. Twenty. Four. Million. Pounds.

There was an initial flurry of viewings, but nothing came of them; it was offered for rental, at £130,000 a month, but there were no takers. So this summer, the owner of Eglon House — who prefers to remain anonymous — placed a call to The Modern House estate agency to see if they could sell it. The Modern House, founded in 2005 by Albert Hill and Matt Gibberd, prides itself on a very different approach to most estate agents. You will never have seen its shops on the high street, because there aren't any. Since the beginning, it has been online only. It specialises in properties it decides are architecturally arresting or allow living "in a modern way".

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Matt Gibberd and Albert Hill, founders of property sales website The Modern House

It used to be said the search for property was all about location, location, location. Hill and Gibberd wouldn't agree with that. To them, contentment is most likely to be found in a beautiful, considered house that allows for open-plan living. And that means you might have to be flexible about where it is. The Modern House is predicated on the idea that many estate agents fundamentally do not understand design and lifestyle.

There are signs that Hill and Gibberd are making some headway in the argument. The Modern House has sold more than 700 properties in the last decade across the UK. On its website now are more than 150 impeccable, elegant apartments and houses to buy. "Statistically, over the past six months we have grown 35 per cent in terms of revenue," says Hill, "whereas Foxtons, Savills etc have all had a negative last six months. So we're doing something right."

At a time when the housing market is flatlining, especially in London, The Modern House is bucking the trend. In the past year, its clean, uncluttered website — closer to an interiors magazine than a property portal — has received almost 3m visits, an increase of 50 per cent on the previous 12 months. Its carefully curated Instagram feed, which features images from houses for sale alongside motivational quotes from modernist icons such as Ludwig Mies van der Rohe, now has over 90,000 followers. These include an above-average proportion of architects, artists and designers.

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Slip House, Lyham Road, London SW2

So it was a smart move by the owner of Eglon House to engage Hill and Gibberd. The Modern House would reach a different audience to Savills and, in its marketing, it would concentrate more on the architectural merit of the building. There is an intriguing story to tell here: Eglon House was designed to be a modern updating of an Art Deco classic called Maison de Verre, built in Paris in 1932 by the architect Pierre Chareau. (In 2007, The New York Times called Maison de Verre simply: "The Best House in Paris.") Mind-scrambling attention to detail had been committed to mirroring the effect in Primrose Hill: this included using the same moulds for the iconic glass blocks that Chareau created for the exterior of his building; the sofas, light fittings, even the exact shade of blue that was used for the master suite's carpet in Paris have been painstakingly reproduced.

"It's mad isn't it?" says Gibberd, who is 40 and tends to wear translucent spectacles and capacious, monochromatic clothing, some of it made by his wife, the designer Faye Toogood. "What an incredibly audacious thing to build." Hill, also 40, slightly less fashion-forward, adds, "It's a one-off. It's amazing."

Appearing on The Modern House can give a property, especially a new build such as Eglon House, a status usually only conferred by a RIBA architectural award. "There's definitely a validation," Gibberd agrees. "And I don't think there are other brands in estate agency that provide a positive image like that. They are coming to us for that, and I think Eglon House is coming to us for our ability just to reach into the cracks between things and access a very unique and powerful network of people. With a house like that, when the conventional route hasn't worked, that's what you've got to do. You've got to think more laterally on the marketing as well." In late October, Eglon House dropped on The Modern House website, now a steal at £21m.

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The first property The Modern House marketed was also an unusual house that traditional estate agents were struggling to bend their heads round. Six Pillars in Sydenham Hill, south-east London, is not especially welcoming or exciting from the front: it is a white rectangle set back from the road, with a thin horizontal strip of window. The main materials are London-stock brick and reinforced concrete, which has been used to fashion the half-dozen pilotis that lend the house its name. And it's these pillars that make this building, completed in 1934, so revolutionary. Because of the strength they provide, the interior can be open and flooded with light. The architects, Valentine Harding and Berthold Lubetkin, the latter best known for the spiral-ramped penguin pool at London Zoo, had been liberated to create balconies that nod to Le Corbusier and staircases that twist like helixes. Lubetkin believed that climbing any set of stairs should be "a dance".

Albert Hill was not even an estate agent when he first saw Six Pillars in 2005. He was a journalist, primarily an editor at Wallpaper*. But he was very familiar with Lubetkin, one of the defining modernist architects, and he couldn't believe that this house — one of the rare private homes in London that Lubetkin had worked on — had been on the market for months and hadn't sold.

"So I got the number of the guy who owns Six Pillars and phoned him up," says Hill. "This was off the back of nothing. I said, 'I've got this specialist estate agency.' He was very well-spoken and he said 'Fantastic, I've been waiting for someone like you to come along.'"

Was Hill completely riffing? "Yeah, just making it up," he laughs. "And he said, 'I'm going away on holiday for three weeks but let's talk when I get back.'"

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Artist Dinos Chapman\'s 7,500sq ft former home in Harrietsham, Kent

In those three weeks, Hill created a website for his new company, and he made contact with a school friend, Matt Gibberd, who had previously been a senior editor at The World of Interiors magazine and had just started in the first year at the Bartlett School of Architecture. There was an element of destiny in his gravitation towards that career: Sir Frederick Gibberd, his grandfather, was a modernist architect who designed the Liverpool Metropolitan Cathedral with its distinctive crown of thorns (you might know it as "Paddy's Wigwam") and the London Central Mosque on the edge of Regent's Park; his father, too, is an architect. Gibberd agreed to start work on The Modern House — the name came from a book written in 1934 by FRS Yorke, a friend of his grandfather's — while also continuing his architecture studies.

Hill and Gibberd used their contacts to get press coverage for Six Pillars, but results were not instant. This, after all, was the era of the Foxtons Mini, ubiquitous in central London, and glass-fronted branches full of aggressive, shiny-suited "negotiators". "I remember in particular one day, I was sitting at home, because we ran it literally from my bedroom to begin with," Hill recalls. "My wife came back, she said, 'How's your day, love?' And I said, 'I'm just playing at make-believe here! The phone hasn't rung.' We were about to pack it up actually and then we got our first sale and suddenly everything snowballed."

Hill and Gibberd, who left the Bartlett after one term, have gone on to nose round, and sell, many of the most notable houses built in the last century. These include private residences by John Pawson, Sir David Adjaye, the house Richard Rogers built for his parents, and a Sixties six-bedroom property in Hertfordshire by the Sydney Opera House designer Jørn Utzon. The Modern House has also created a market for apartments and houses that were unloved, or viewed as eyesores, when they started in 2005. They won't be to everyone's taste, but brutalist blocks such as the Alexandra and Ainsworth estate, a Seventies social housing scheme built in north London by architect Neave Brown, now regularly feature on The Modern House's books and have lines round the block on viewing days.

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Neave Brown\'s Ainsworth Estate, Rowley Way, London NW8

"Those flats are absolutely hoovered up now by design-conscious first-time buyers because they recognise you just get more space and it's more useable space," says Gibberd. "It's not like a Victorian conversion where everything's carved up and it's got staircases everywhere and thin walls and you can hear everyone else. One of the achievements I'm proudest of with The Modern House is we have genuinely created a platform and a market for these places that wasn't there before. As a result, their value has risen."

The Modern House has also been at the forefront of an unlikely phenomenon: people look at their website for recreation, even when they have no active interest in finding a place to live. "Property porn" was added to the dictionary in 2005. "The word porn means you probably feel a bit bad about doing it, you feel a bit guilty about it," says Hill. "But it's really about aspiration, isn't it? Looking at things and thinking, 'Oooh.'"

This could, of course, lead to the charge that The Modern House is likely to attract a disproportionate number of time-wasters. Hill, though, disagrees. "Yes, there's loads of people looking at our site and they've got no intention of buying or selling," he says. "But they know someone who does. And when we do all our research we sell so many places to people who say, 'A friend said I had to look at this place they'd seen through The Modern House.' So we've got a whole army of promoters out there."

Perhaps the greatest satisfaction Hill and Gibberd have, though, is that in their small corner of the market, they are rehabilitating the tarnished image of estate agents. The Modern House carefully tracks its Net Promoter Score: this is a customer-loyalty metric that rates companies between +100 (everybody loves you) and -100 (Ryanair); a mark of excellence is felt to be anything over 50. The Modern House currently has a NPS of 98.