Ever since the graffiti artist Banksy smuggled a dead rat into the Natural History Museum and mounted it as an exhibit in a glass-fronted box, his mischief-making has been surpassed only by his talent for making money. Lionised by Angelina Jolie’s hip crowd in Tinseltown, the once scruffy street urchin from Bristol astonished the art world last week by breaking his own auction record.

The secretive “guerrilla artist” pocketed £58,000 for his version of the Mona Lisa, with spray paint dripping from her eyes, and £50,000 for six prints of the model Kate Moss, executed in the lurid hues of Andy Warhol’s Marilyn Monroe series. A year ago an edition of the Moss prints was on sale at his rat-infested warehouse in west London for a mere £1,500.

Who is Banksy? Nobody really knows. He has been named as Robert Banks and is believed to hang out in east London’s arty milieu of Hoxton. But he now calls himself Robin Banks, an anarchic joke that has been given new meaning by the willingness of frenzied bidders to throw money at him. When one of the few journalists to have a face-to-face interview with him demanded, “How do I know you are Banksy?” he replied, “You have no guarantee of that whatsoever.”

“Banksy” is also the nickname of Gordon Banks, the England goalkeeper and hero of the 1966 World Cup, but this possibility was ruled out by another interviewer who described the elusive prankster as a dark-haired man in his early thirties, lightly bearded and wearing “nice trainers”. Banksy insists that even his parents think he’s a painter and decorator. Asked why he clings to anonymity, he said: “So I can do my work without being impeded by arrest.”

Some people, it is true, would like to see him safely confined. What began with belly laughs when he infiltrated the penguin enclosure at London Zoo and painted, “We’re bored of fish”, followed by his message in Bristol Zoo’s elephant enclosure, “Keeper smells”, shaded into outrage when he began painting on live animals. Last year he placed subversive artworks in four New York museums and did an unauthorised decorating job on the Israeli West Bank wall.

His stunt spree this year included replacing up to 500 copies of Paris Hilton’s debut album with remixes and his own cover art depicting the model topless, and sneaking into Disneyland to leave an inflatable doll dressed in the orange uniform of a Guantanamo Bay detainment camp prisoner.

All of which has made him one of the few Brits to have cracked America. “These days everyone is trying to be famous, but he has anonymity,” marvelled the actor Brad Pitt. “I think that’s great.” Pitt and his squeeze, Jolie, opened their arms and wallets to Banksy at his Los Angeles show Barely Legal last month, along with special guests Keanu Reeves, Jude Law, Christina Aguilera and Macaulay Culkin.

Helped by an Asian elephant, painted with a pink and gold flock wallpaper motif, the show was a hit and earned Banksy a reported $3m. But was it a moral sell-out by the self-styled anti-capitalist who claims he is not motivated by money? As usual, Banksy, who did not deign to turn up at the show, had a disarming answer: “Hollywood is a town where they honour their heroes by writing their names on the pavement to be walked on by fat people and peed on by dogs. It seemed like a great place to come and be ambitious.”

Banksy has always created enough mayhem to stay just ahead of such criticism. His dead rat prank in 2004 was a classic. Disguised as an employee of the Natural History Museum in London, and bearing a stuffed rodent clad in wraparound sunglasses, he mounted his exhibit with a nail, but had to use heavy duty glue when it would not hold. It was nearly a repeat of his earlier flop, when his illegal exhibit at Tate Britain came crashing down because the glue was too weak. But this time it remained intact for several hours before staff noticed the graffiti legend above it: “Our time will come.”

Last year Banksy grew more ambitious, targeting the Brooklyn Museum, the Metropolitan Museum of Art, the Museum of Modern Art and the American Museum of Natural History. Website images show him in a Toulouse-Lautrec fake beard and pensioner’s clothes as he installed his own works, complete with name plaques and explanations, on the hallowed walls. They included a tin of Tesco tomato soup and a Victorian lady in a gas mask. “They’re good enough to be there, so I don’t see why I should wait,” he declared.

Soon after, his version of a primitive cave painting depicting a hunter pushing a supermarket trolley was found hanging in the British Museum. The archivists rather spoiled the effect by adding it to their permanent collection.

Then Banksy surpassed himself by tackling Israel’s 425-mile wall. With the help of Palestinians, he painted nine subversive images, including a ladder going over the barrier and one of children digging a hole through it. Why did he do it? In a telephone interview with The Sunday Times, he explained: “If you are slightly obsessed about painting on walls, you are likely to want to paint on the biggest wall in the world.”

The Palestinians, he recalled, had cheerfully sent him up the wall, “waiting for the whitey to fall off” and abandoning him at the first sign of Israeli soldiers, who let off warning shots. His hosts were bemused by his efforts. “When I painted a living room scene with a window looking onto an alpine view, they said, ‘So, when are you going to paint Ariel Sharon dead in the armchair?’” Another local remarked that he was making the wall beautiful. Banksy thanked him. “We don’t want it beautiful,” the man spat. “Go home.”