“There can be something beautiful,” Richard Wilson tells me, “about destruction.” To demonstrate, he has just installed a strange and arresting artwork at the London School of Economics.

I arrived at Kingsway, London’s stiff, imperial attempt at a Parisian boulevard, to see construction workers craning in a new corner. It was a curious sight: the roads were clogged with tourists and office workers looking bemusedly on. What Wilson has done is to “finish off” the architecture. The building formerly featured a chamfered corner; he has built it out to 90 degrees again but has also crumpled it up at the base so that the pavement corner retains its original shape, with pedestrians passing under an unsettlingly static mass of rubble.

“I hate the expression ‘public sculpture’,” Wilson says. “It implies something second-rate, something that goes into municipal parks. I make work outside. All art was public until it was taken into the galleries in the 19th century.”

Wilson is one of Britain’s most respected and challenging contemporary artists, working with architecture and installation. He has made some of the most memorable and arguably the best “outside” works of recent years. There is “Slice of Reality”, a cutaway section of a ship standing beside the Millennium Dome, a ghostly memory of a departed industry (in which the artist now has a studio). There is “18 Holes”, a series of squat structures on Folkestone’s seafront, little houses that look like concrete beach huts but which, on close inspection, reveal walls and roofs built of the cut-up remains of the town’s mini-golf course, complete with holes.

Most memorably of all, there is “Turning the Place Over” in Liverpool, a circular chunk of office block façade that pivots and revolves through three dimensions within a derelict modernist building. Commissioned for last year’s Liverpool Biennial, it is still turning and has become a kind of cult presence, making something beautiful and compelling from an otherwise invisible piece of generic modern building.

All Wilson’s work plays on architecture, each builds on its context through surprise, incongruity, humour and a pervasive sense of unease. And it is this uneasiness that is most visible on Kingsway. The artist has extruded the structure but in doing so has formed a hybrid generic section (he calls it a “Toblerone”) which is simultaneously right and utterly wrong.

Abstracted from two other bits of Kingsway, in scale, colour and style it matches its Edwardian setting but is slightly out of sync: its slightly sinister blind windows are too close to the corner, breaking the impeccable symmetry that was at the heart of this Beaux Arts architecture. It is very slightly apart from the old building and the gap is subtly illuminated at night; it is a corner that floats, the very thing a corner should not, intuitively, do. There is an intimation of disaster – an earthquake, a bomb, a moment of collapse captured.

“I don’t feel the building is exploding,” Wilson tells me, “but it’s revealing itself, existing in these two states simultaneously.” There is nothing new about building apparently collapsing structures, from the picturesquely ruined follies of the 18th-century garden to Gordon Matta-Clark’s slicing through existing buildings to form new works of art in the 1970s, to MUF’s recent and delightful faux ruin in Barking, east London. It was one of the defining features of the “deconstruction” that spread like a virus through architecture in the late 1980s. But that doesn’t make Wilson’s work any less arresting and it is precisely the banality of its context, the ordinariness of Kingsway’s approximation of Parisian grandeur, that allows it to work so well.

“Architecture,” says Wilson “is order” – interfere with it, and nothing is certain anymore. What a metaphor to extrude out of a school of economics.

‘Square the Block’ was commissioned by the Contemporary Art Society