W hen it starts raining on the slate roof of the Grade II-listed, late Georgian north London house where the architects Anna Liu and Mike Tonkin have their home and office, it gathers in a black downpipe on the rear wall. This is normal. What happens next is not. Before it gets to the bottom, like a stunt plane exiting a death dive, the pipe turns, curves and then swoops into a more shallow descent, then goes up a bit, then down again, before terminating in a non-figurative gargoyle about two metres off the ground, from which the rainwater, after a delay while it gathers enough pressure to push itself through the elaborate pipage, then gushes.

Which turns out to be only one move of several in an architectural rain dance. The gargoyle discharges into a long black steel trough that, if a switch is flicked, then overflows via concealed pipework in such a way that water starts rising through the joints between dark granite paving in a small courtyard. Should it be night-time, horizontal lasers can be switched on, which capture drops with illumination as they fall and bounce. If it’s day and the sun comes out, rippling light will reflect off the wet paviours, bouncing around surrounding surfaces of glass, mirror and whiteness. All this irrigation and solar energy eventually manifests itself as vigorous vegetation, a touch exotic and tropical, some of it growing out of the planted roof that partially encircles the court.

The Sun Rain Room, as this work is accurately called, may be the architectural project with the most meteorology per square metre since Noah built the ark. The architects say they want it to be “a good place to be on a bad day”. Because of the doubling and dissolving of the reflective surfaces, it takes a while to realise how little usable space is actually added – just a big wall cupboard to house a barbecue, a potting shed and such like, an enclosed area big enough for a smallish dining table and another, sheltered but external, where you can also eat. Mostly, it’s a machine for enjoying the weather.

There is also a room underneath, the bedroom of a basement flat, added late in the gestation of the project when it became clear that the mathematics of property prices in the London borough of Islington would more than repay the cost of construction. It is thus a (relatively modest) addition to the new basementism that elsewhere in the capital has seen swimming pools and vintage car collections put underground. But here the main object of the work – which has taken 12 years to complete since it was a gleam in Tonkin and Liu’s eye, and whose cost of £235,000 would be much greater if they hadn’t put a lot of their own time and ingenuity into the construction – is to allow the full enjoyment of a small London garden that somehow they hadn’t used much.

Its style, superficially, is a sort of retro-futurism, the 21st century as seen from the 1960s and 70s, a bit Kubrick, a bit Woody Allen in Sleeper, white and swooshy, engaging but hard now to look at without the condescending thought that the future didn’t turn out quite like this. Tonkin Liu, who made their name with a series of singular private homes and makeovers of public spaces, are fond of this style, though they’re fluid enough not to be a one-look practice. There is a bit of it in a bridge they have proposed for Salford, and the interiors of a clifftop house in Dover.

The Sun Rain Room is also more than this. Tonkin refers to his early years working for an architectural reclamation company in Bath, where he “learned so much about classical detailing”. While there is absolutely nothing neo-Georgian about their design, he says, it has picked up cues from the house it extends, taking, for example, twists and curves from the old stairs and banisters. The architects also say they’re re-enacting on a smaller scale the interaction between hard architecture and lush planting that you get in the composition of the town square their house faces, with a big garden in the middle.

The curving ceiling around the edge of the courtyard is punctured by small, glass-domed holes that admit discs of light, like little suns. The holes are at the end of inverted lunar craters whose curved concentric contours are then picked out in fine relief. The repeating curved lines consciously echo the waves of reflection that play across them. They modulate light and shadow in a way somewhat like the subtle recessions and projections of Georgian glazing bars and panelling.

The old house itself is mostly painted white, with mirrors inset at opportune moments – behind shelves, in cupboard doors – such that they dematerialise the walls and fold views of external greenery and weather into the interior. They help to set up a continuum of light, reflection and dissolving surfaces that, while it’s clear where the old stops and the new starts, runs from the square garden through the house to the back of the Sun Rain Room.

It has required patience and effort to achieve – negotiating the legalities of small London sites with many neighbours, waiting for financial stars to align, managing the construction themselves to keep costs down, working with sympathetic subcontractors. Two leading engineers have made possible the project’s structurally ambitious ideas. One, Tim Macfarlane, assisted with an all-glass staircase that maximises the light reaching the basement and glows at night with light coming from below. Another, Rodrigues Associates, has helped achieve the exceptionally thin profile of the curving roof. Its plywood structure was assembled with the help of students from three London architecture schools.

In the end, the hard construction and hard work serve intangibles and subtle substances such as light, atmosphere and nature, things that, as Tonkin and Liu say, “don’t cost anything”. A world is constructed of dissolution, floating, evanescence and inversion in which opposites combine. There are plants on the roof and water on the floor. The stairs are glass. It’s techno-natural and futuro-Georgian.

With so many ideas in a small place it could all be too much. With so many devices and contraptions, there’s a risk they might not function as well as advertised. But one of the impressive things about the Sun Rain Room is the degree of thought given to things like proportion, lines of sight and the shade of materials to put behind water, such that its drops and ripples become visible. It works.