You never see a lone guardsman. And never out of context, in the streets of the financial district, far from barracks or palace ceremonial duties. He holds his gun slackly by his side. His body language speaks of slight dejection. He stops and stares in the window of a Next fashion store, as if pondering a switch to smart-casual clothes. He sits on a bench and brushes his bearskin with the rough affection of a man for his dog. The CCTV cameras, you can tell, are worried. He shouldn't be here. He's carrying a serious weapon. They pan and tilt to follow him.

Slowly you realise, as the film cuts from scene to scene, Barbican to Mansion House to Guildhall to medieval alley, that this is not one solo guardsman. There are many, and they are all trying to find each other. Eventually, they do. A guard meets another. They pause, straighten up, shoulder arms, get into step, march away with purpose. As soon as there's two, they are a unit. They clearly feel better. And as they gradually coalesce into steadily larger groups, they get happier still, marching with zest through the City streets. For some purpose we can only guess at.

This is the sidelong world of artist Francis Alÿs, and this is part of his complex and highly-nuanced response to London, this year's major commission from the Artangel agency. Alÿs is Belgian-born - surrealism is in his blood - but based in Mexico City. He walks around it and other world cities, and then makes his responses to these walks into works of art. He does this in various ways - film, drawings and music being among them. He is regarded by many - including Artangel's co-director James Lingwood - as one of the world's most significant contemporary artists. This is his first U.K. commission, and it has taken five years to bring it to this point.

Sometimes he is the protagonist: another short film shows him rattling a stick along the railings and porticoes of architect John Nash's Park Crescent. He does it seemingly casually, puffing a cigarette as he goes, a scrawny figure in a raincoat, but actually keeping to a strict tempo. Then the film cuts to Onslow Gardens in Chelsea - lots more railings there - where his stick-rattling becomes an accomplished, syncopated percussion piece. Railings, he has noticed, are a very London thing.

He is equally likely to recruit the inhabitants of his chosen city, knowingly or unknowingly. While getting to film 64 Coldstream Guards in the City was a daunting logistical exercise taking years to set up, finance and accomplish (the Outset Contemporary Art Fund was a big help there) following a West London milkman around as he made his doorstep deliveries was rather simpler. In the resulting film, "Milk and Ice", Alÿs simply intercuts that footage with similar deliveries in Mexico City - but in that case, it is large blocks of ice being distributed, for use by street traders. In both cases, Alÿs is fascinated by the fact that such useful commodities - which coincidentally would help each other, were they together in the same place - can be just casually left around a cityscape. Regarded as normal by the inhabitants, they become exotic, puzzling deposits to outsiders.

Duality clearly intrigues Alÿs: he also went through London parks taking photos of those who sit in the sun, and those who sit in the shade, finding that light-skinned people for some reason preferred sun. Is this a racial thing, a tourist-versus-resident thing, or just force of habit? He offers no comment, just the images. He makes his art in all sorts of ways. He has, for instance, made a painting of commuters' feet. Unremarkable in itself, it takes on a significance when he gets people to take the painting home from the gallery every night, look after it, and bring it back the next morning. It becomes the act it depicts.

These gentle, ironic looks at London are informed by an architectural sensibility - Alÿs originally trained as an architect, and it shows. He picks up on street furniture, paving patterns, noting such things as that many of our bollards are modelled on captured cannon, or that the scary heraldic beasts that still guard the City are now backed up by extraordinary numbers of CCTV cameras (they don't have those in Mexico City, he says - people wouldn't stand for them, and they'd only get stolen).

At one point he wanted to make a film out of the millions of hours of CCTV footage recorded in the City, but found that although you are legally entitled to see the images, you are not allowed to use them. So instead, he has worked with the National Portrait Gallery to make a piece generated by its own state-of-the-art internal CCTV system. He released a fox, called Bandit, into the deserted gallery at night. The resulting film as seen from the high viewpoint of the security cameras shows the fox, trotting from room to room, pausing, sniffing purposefully or just looking a bit puzzled on the polished floors among all the paintings of the great and the good. Like the guardsmen, he (or she) is out of context, an intruder, observed dispassionately. The choice of a fox - an animal about whom humans are ambivalent - is apposite, the title of the film ("The Nightwatch") loaded. The artist's approach feels just right: raising questions in your mind about the nature of surveillance while simultaneously subverting these instruments of social control.

The bulk of the show, however, is in another very London place: 21 Portman Square, a 1772 James Adam house that was until recently the home of the RIBA's Heinz Gallery and its world-class collection of drawings and models, now moved to the V&A. Thus deserted and stripped back to its peeling ceilings and 1970s colour scheme, the house is - like much that Alÿs observed here - a faded echo of a greater, imperial past. His slow-burn observations are acute: he has captured us, totally.

Behind and beneath everything, including the machinery of state and entrenched customs, Alÿs seems to be saying, is the individual. His wandering Guards in the City eventually form a precision military marching machine, a perfect square of 64. Then they break step and disperse over Southwark Bridge, chatting and slouching. Suddenly they are just a bunch of ordinary blokes again. But no longer alone, and no longer a potential danger.

"Francis Alÿs: Seven Walks" is at 21 Portman Square, London W1, and the National Portrait Gallery until November 20 2005. Artangel website:. www.artangel.org.uk