I know that this mammal has become pretty metropolitan these days. But this particular creature hadn’t simply popped in to admire a few portraits, to sniff at the sables and ermines of Elizabethan forebears. It was part of an artwork by Francis Alÿs.

Alÿs, who is based in Mexico, was invited by the pioneering arts organisation Artangel to work on his first British project. For month after month he paced the streets of the capital in search of inspiration. And one of the things that most struck him, it emerges as you visit his exhibition (it opens today, both in the National Portrait Gallery and amid the faded neoclassical splendour of 21 Portman Square), was the omnipresence of surveillance cameras. With more than half a million of them, London apparently exceeds any other capital except Seoul. They seem to breed — a bit like the foxes — in the interstices of the city. Skulking in porticos, protruding from alcoves, spying from lampposts and invigilating our parks, they scan our routines with an unblinking electronic eye. The average commuter is captured on film as many as 300 times an hour. London is no place for the camera shy.

Of course this feels disconcerting — not least when you read of all the sci-fi-style technology in development: the directional motion sensors that will isolate anyone with a course set against that of the crowd; the backscatter X-rays that strip-search you as you enter a subway; the chips that can analyse the halo of heat you emit. But as fears of terrorism mount, the march towards a surveillance society seems almost compulsory. Our privacy is increasingly sacrificed. Is it worth it? At the moment the debate looks set to continue indefinitely.

But at least what Alÿs — and the many other artists who incorporate surveillance techniques into their work — can show us is that the prying camera cannot cramp the imagination. Technology cannot impinge on the lands that lie locked inside our heads. Maybe it can even drive us down deeper into the burrows of our individuality; help us to discover more closely the true lair of our selves. So, who cares about reality TV? We have TV reality. Play with the idea. Camp it up for the camera. Treat the streets as your stage. Look up: give your foxiest smile to the lens.

• SURVEILLANCE will be very much encouraged this weekend. Sunday sees the launch of The Big Draw — a nationwide, month-long celebration that encourages everyone to explore the powers and possibilities of the draughtsman’s talent. (Visit www.thebigdraw.org.uk for details). As part of the carnivalesque kick-off in Exhibition Road, South Kensington, Sarah Simblet, a tutor at the Ruskin School in Oxford, will be offering life-drawing classes. She firmly believes that, regardless of inborn talent, it takes only a couple of hours to imbue anyone with confidence, to ignite their interest and hopefully inspire them to go on.

  “By drawing the world around us we learn to see it,” Dr Simblet assures me, as I stand, eyes flummoxed with effort, in front of the charcoal-smudged paper on to which I am frantically scrubbing the image of a chilly but stoical nude model. “Drawing is the immediate expression of seeing, thinking and feeling. It is a mirror through which I understand my place in the world, and through which I can see how I think,” she says.

  My thinking, it seemed to me, was decidedly squiffy. But what I was starting to understand was that the watchfulness of drawing serves a very different purpose to that of the surveillance camera. It is far less about selecting, about isolating the detail, than about seeing the pattern, the way all the elements interrelate in the puzzle. If the lens tends to breed a mood of detachment, drawing encourages us to draw closer, to try to connect.

• ATTUNED, maybe, to the idea of surveillance, I listened in to the conversation of two girls on the train to Oxford. “Look, we’re nearly there,” one of them suddenly sat up and said. “I can see the Tesco tower.” It was a sad day for the city. Whatever happened to the dreaming spires?

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