British zoos have been warned their rhinos may be attacked by poachers because of the soaring value of their horns in the Asian medicine market.

After a rumour that it could cure cancer, the horn is now worth more than $40,000 a kilo, and gangs have been breaking into museums and auction rooms in Britain and Europe to steal trophy rhinoceros heads. The fear is zoos – and live rhinos – may be next.

In an unprecedented alert, all 15 British zoos and wildlife and safari parks which hold rhinos – they have 85 animals between them – have been warned by the National Wildlife Crime Unit to tighten security and report anything suspicious to the police at once.

"We have warned British zoos to be on their guard against the possibility of being targeted by criminals seeking rhino horn," said the head of the unit, Detective Inspector Brian Stuart.

Concern is growing that criminals will try to break into a British zoo at night, kill or tranquillise rhinos, and cut off the horns. The potential profits might be very tempting, as a single big horn could weigh more than 5kg and be worth more than $200,000.

In the past four years rhino poaching has exploded in Africa – South Africa especially – going from a total of 13 animals killed for their horn in South Africa in 2007 to 448 in 2011, the highest number ever recorded. Twelve have already been killed in South Africa this year.

The head of Biaza (the British and Irish Association of Zoos and Aquariaums), Miranda Stevenson, said she was "horrified" at the threat, but that, while security made it difficult to get into zoos, "it isn't impossible. Rhinos are big animals and in good weather most zoos will leave them out at night."

A source from a big zoo in southern England said: "We are aware of the warning but our security is pretty tight. We have keepers living on site and they make night patrols."

Detectives first became aware of the threat to zoos after a man was caught trying to smuggle a rhino horn out of Britain to Asia – which turned out to have come from an animal which had died of natural causes in Colchester Zoo.

Powdered rhino horn has long been used as an ingredient in traditional Asian medicine, where it is reputed to lessen fevers.

However, an urban myth about a senior Vietnamese politician who reputedly had his cancer cured by rhino horn swept across Asia in 2008, even though the politician has never been identified or come forward.

Andrew McVey, Species Programme Manager at WWF-UK, said, "A lot of effort is going into addressing the poaching, but we have not been as successful as we would like to be," he said.

The knock-on effects have involved almost 50 targeted burglaries of museums holding rhino heads in Britain and the Continent.

Last July, burglars broke into Ipswich Museum and sawed the 18in horn off Rosie, the head of an Indian rhino that had been there since 1907.