There is an image in the late historian Alan Colquhoun's book Modern Architecture which marks the point where the apparent differences between actual lived space and painting have been turned upside down. The image shows three plans for houses by Mies van der Rohe of 1923-4 – the Concrete Country House, the Lessing House and the Brick Country House. Mies, who had previously designed several country houses in Germany, at first provides with the Concrete Country House a more abstracted, rectilinear version of the 'house', where its twists and turns are no longer dictated by the need for load-bearing walls. Then, with the Lessing House, though you can see the plans of the rooms that will go in the house, the formal geometry starts to resemble something that isn't dictated by what will go inside the plan, but by the plan itself. Then, suddenly, with the Brick Country House, the plan has been exploded, and any surviving referent to the idea of the 'house' is far distant. Colquhoun writes that 'closed volumes have disappeared and the space is defined only by free-standing planes, as in Theo van Doesburg's Counter-constructions.' That is, Mies has designed a house as if he is creating an abstract painting, with the image of the Plan more important than the inhabitation of the house itself, where the overarching plan will not be entirely visible. Or rather, the plan would be visible, but in the most abstracted way. The lack of closed volumes means that the house would be experienced as a sensation of objects in space – something Mies achieved most fully in his Pavilion for the Barcelona expo of 1929. So as early as 1924, the line between abstraction and life has been decisively crossed.

In some ways, there's nothing particularly new about the idea. The 'architecture parlante' of Claude-Nicolas Ledoux entailed a fair few illustrative plans – most famously, in his plan for the town of Chaux, a brothel whose plan was in the outline of an erect penis. Regimes with a taste for symbolism have also often indulged in the practice – in the 1920s Soviet Union a fair few buildings were designed in the shape of the hammer and sickle, including a housing scheme for the secret police (why? Was the idea that the shape would remind them of communist virtue?), and in the following decade Moscow's Red Army Theatre was designed in the shape of a star, something that surely can't have been helpful for its acoustics. In all of these cases functionality – including in the brothel – can surely only have been impeded by aestheticising the plan. What Mies was doing was something rather different. He wasn't solely dissassembling and abstracting his country house because he thought it would be nice idea for a house's plan to look like a De Stijl painting. It was more because he saw something in those paintings which could be translated into a particular experience of real space. It's in this conjunction perhaps that Keith Coventry's series of Estate Paintings, running from 1992 to 2007, can be seen as something other than a clever art-historical joke. What if they're not merely 'about' the decline of a particular idea into the mundanity of council estate layouts, but are instead a reminder of the way a conception of space taken from the avant-garde is now part of everyday life? 

It's interesting in this respect to compare Coventry's paintings with those of his near-contemporary, the architect Zaha Hadid, as both draw very closely on the work of Kasimir Malevich, El Lissitzky and the Soviet Suprematists – and both have applied those ideas to actual areas of south London. Malevich is usually the artist to whom Coventry's Estate Paintings are compared, and for fairly obvious reasons. From 1913 on, Malevich's Suprematist paintings of objects floating, careering and intersecting in white space developed from a new idea of painting into a new idea of the world. From their base in Vitebsk, Belarus, the UNOVIS artists applied the spatial ideas of Suprematism to everything from political posters, interior design, the decoration of city squares, and eventually to architecture. However, it should be noted that when it came to designing prospective buildings, Malevich abandoned these weightless volumes floating in space, and instead opted for something much more weighty. His architectural sculptures or 'Architektons' were actually oddly heavy, based more on a compacted sense of mass and power rather than spaciousness. Nonetheless, the work of Malevich's successors such as Alexander Vesnin, Iakov Chernikhov or Lazar Khidekel did apply his spatial inventions to the more prosaic matter of floorplans for workers' clubs, factories and blocks of flats. The spaces inbetween, white on the canvas, were usually green in the completed schemes, filled with trees and vegetation. Fifty years and a few rediscoveries and revivals later, Hadid and Coventry took up Malevich and architecture in contrasting ways. In the early 1980s, Hadid proposed a scheme called 'Malevich's Tektonik' for the South Bank of the Thames. Her vivid painting of the scheme is, more or less, a Suprematist painting that refers to architecture rather than an architectural drawing as such. Hungerford Bridge has become a stepped, multi-level, multi-functional Architekton – and to the south, the Hayward Gallery, Queen Elizabeth Hall et al are represented by and extended through abstracted volumes, exploded across the former Festival of Britain site. Regardless of the extreme talent evident in the painting and the architectural proposal, what Hadid does is take what appears to be a high art idea, and apply it to an area of London where high art is produced and consumed.

What Coventry does, conversely, from the earliest of the Estate Paintings onwards, is reveal that high art lies behind the lowest-class areas of south London. The maps on every council estate in the UK, helping the pedestrian make sense of their non-traditional layout, are quite simply stripped of names, council logos and municipal colour schemes, and are rendered on white space in Malevich-approved bright primary colours. On one level, it's just a typically '90s gag. You're looking at the painting that seems to be a lost work by Malevich (and remember here that plenty of fake Russian avant-garde paintings were circulating after the collapse of the USSR), and then your eye travels down to the bottom of the frame, where you see 'SCEAUX GARDENS ESTATE'. Ha ha. You have successfully revealed yourself as knowing more about art history than about the area directly around the gallery. There is more happening here, though. The very reason why that map looks like a painting by Malevich is because those who planned these estates were rooted, at one remove or none, in the ideas of Malevich.

In an interview with William Furlong, Coventry says that 'I'm interested really in looking at aspects of art history and grafting on to them some kind of social issue, so that the two seem to make a comment upon the other. I've looked at the Russian Constructivists – Malevich and so on – and how they tried to create a world that was pure through their work, but they actually failed at doing that. They set up a kind of revolution in terms of ideas about mass housing, and that led to the sort of social problems that we have now through the construction of those schemes'. Now obviously there was mass housing before Malevich and the Constructivists, but it was usually either constructed by speculators for rent in the nineteenth century, much of it too dense and grid-planned to make its way into a disguised Suprematist painting – or, it was constructed by charities and municipal reformers in looping, curving cul-de-sacs. In both cases the schemes were based upon streets, and upon getting as much housing into the site as possible, in order either to make as much profit from the site as possible or in order to cram as many people on the waiting list as feasible without having to build flats. Neither of these versions of mass housing needed to provide maps for people to get around. The revolution that Coventry is talking about, and about which he is evidently sceptical, was about trying to create that painterly empty space that Mies had translated into the house – in something as straightforward and important as a council estate.

It's this space, the space that is the white-on-white backdrop to all of the estate paintings, that has helped to make so much modernist planning enduringly controversial.  Its beginnings are in Le Corbusier's Ville Radieuse, of course, but maybe more influentially the Zeilenbau or row-building adopted by bauhaus director Walter Gropius for the Dammerstock housing estate in Karlsruhe. This envisaged long linear blocks in parkland, arranged in rows, with parkland inbetween. What was the parkland for? Not much, claimed Jane Jacobs in the 1960s – fit for little than for 'Christopher Robin to go hippety-hoppety', an anti-urban dead zone based on a profound misunderstanding of the density of street life needed in cities. Jacobs, in the Death and Life of Great American Cities, appeared to take the view that it wouldn't make much difference if the spaces inbetween really were a white, endless void, as they are in the Estate Paintings. People, she claimed, did not use the specially-allotted green spaces, didn't sit under the trees or on the benches. They preferred to experience street life in a more informal way, sat on the steps to their tenements, chatting outside market stalls, hanging around on the high street. The white/green spaces were an idea of public space, not a real and viable form of public space. In this, there's an element of bitter satire underlying the Estate Paintings. Look at his 'Coopers Road Estate' of 1995, where six red blocks, two long, four short, are lost, adrift, in a sea of white Suprematist empty space. How do you actually manage to live in that? Given that the estate was demolished and replaced with something more intuitive, dense and straightforward, it would seem that the narrative of 'failure', the sense that the paintings depict the dire consequences of utopianism, is unavoidable.

Is it really, though? Another of Coventry's paintings depicts the Heygate Estate in the Elephant and Castle, its four rectangles arranged as a particularly sharp piece of Constructivist geometry. The apparently dead space runs inbetween. But, peculiarly enough, the residents of the estate who have been campaigning to try and halt its demolition (and their very real replacement with housing for a 'better class' of resident) have often pointed to the spaces between as their reason for appreciating and enjoying living in the estate. It isn't just white and blank space, but instead is full of tall trees, birds, light, air, openness...a sense of being both in an ultramodern complex in the heart of the city and in an oasis of calm and informality. The new blocks that will be replacing the Heygate will be considerably higher density in order to maximise the extractable revenue, and that space between – that enduring legacy of the avant-garde in mundane south-east London - will be the first thing to disappear. There is a Belgrade-based group, World Communal Heritage, who travel around estates in the former east and west of Europe, placing maps and plaques on the site of modernist public spaces which seem particularly green, impressive and usable, and that are in particular danger. In London, they chose the Heygate, and issued a manifesto. 'Here there are no safeguards or fences that could slow down your pace! You can gather together without paying a fortune for the gentrified lifestyle in the inner-city! The openness, porosity and communicability of Modernist social architecture and landscaping takes shape in a wealth of free space, pedestrian pathways, bridges, passages, niches, little woods and bushes, giving the possibility of direct action. So let’s take it!'. That's a legacy of the avant-garde in the estates of south London just as legitimate as that of the Estate Paintings. Rather than a failure best forgotten about, perhaps it represents the avant-garde's greatest success?