An urgent campaign has been launched to capture up to 20 beavers that have colonised rivers and lochs and are freely breeding in the wild.

The unpublicised project has been authorised by Scottish Natural Heritage, the government wildlife body, after it emerged that a large number of beavers had taken root following a series of escapes from private collections in Angus and Perthshire over the past decade.

Some wildlife experts believe that more than 50 beavers could be roaming free: families of beavers, and evidence of their lodge building, have been regularly seen by villagers and naturalists around Invergowrie on the outskirts of Dundee, Forfar in Angus, Glamis in Perthshire, and Tentsmuir near the mouth of the river Tay.

The animals will be trapped and given to the Royal Zoological Society of Scotland, which houses beavers at its Highland wildlife park and is closely involved with the UK's only official beaver reintroduction scheme at Knapdale forest in Mid-Argyll.

But pro-beaver campaigners have furiously attacked the trapping exercise, accusing the conservation agencies of bowing to political pressure from landowners and urging the protection of the Knapdale project to avoid it being damaged by rows over illegal releases.

Sir John Lister-Kaye, a former president of the Scottish Wildlife Trust who keeps beavers at his Aigas wildlife sanctuary near Inverness, said the animals were once native to the UK and should be given protection under European conservation directives if they were breeding successfully.

"I think this is quite simply professional jealousy. Scottish Natural Heritage and the zoo have been quite hostile to those of us who have private collections or who know quite a lot about beavers," he said. "I think the public needs to be in on this debate; they've voted 59% in favour of the beaver."

His criticisms were shared by Paul Ramsay, who owns captive beavers at Alyth near Dundee. He admitted some of his animals had previously escaped but said that wildlife laws were clear: if a previously native species had re-established itself and was healthy, then it could be legally protected. "I think it's extraordinary that they should take this hostile view," he said.

SNH said the trapping operation, which is being supported by Tayside police, was a matter of urgency because beavers were spreading so rapidly. A spokesman said: "The longer we leave it the greater the task will be. We are also urging all owners of animal collections to take greater care in keeping their animals captive."

The controversy highlights a long-standing but rarely discussed problem across the UK, with persistent escapes from private beaver collections and wildlife reserves over the past 20 years, many of which have been covered up or gone unreported.

The Guardian has established that at least 20 beavers are known to have escaped from collections across southern England, the Midlands and Scotland. In some cases, the beavers were either quickly trapped and returned to captivity or believed to have been killed. However, naturalists are convinced they have now established colonies in the wild in the Scottish Highlands, particularly on Loch Tummel and on the Tay and its tributaries, but also potentially in southern England.

In parallel, conservationists in Wales and south-west England have been planning their own legally sanctioned beaver reintroduction projects, but these were being drafted before last month's deep cuts in government spending on environment programmes.

In Knapdale, there are now four beaver families living and breeding on a network of remote lochs in an uninhabited area of ancient forests bordered by the sea and the Crinan canal. If the trial succeeds, the Scottish Beaver Trial partnership has suggested eventually releasing them at Insh marshes in the Cairngorms.

SNH said it had little choice about taking action on Tayside: none of the releases in the region had been licensed as required by the law. International guidelines are strict about the need for proper consultation and evaluation before locally extinct species are reintroduced.

"They are being recaptured because their presence in the wild is illegal and because their welfare may be at risk," a spokesman said. "There was no consultation with local people; there was no licence issued for their release; there is no monitoring of their welfare; and there is no certainty that they are the appropriate species or type of beaver for Scotland." That claim was contested by Lister-Kaye, a former chairman of SNH's Highland regional board, and by Ramsay. They said their beavers were Bavarian and from a much stronger and more varied genetic stock than the Norwegian beavers released at Knapdale.

The Norwegian beavers came from a much smaller group of closely related animals, and were more prone to disease and genetic problems. But since they are all European beavers, they are related to the animals which once lived in the UK and were suitable for British conditions. SNH disagreed.