GREY squirrels and deer which are wreaking havoc on woodlands and their wildlife need to be controlled, landowners have urged.

The call from the Country Land and Business Association (CLA) to tackle the invasive grey squirrel is backed by the Prince of Wales, who said it was "absolutely crucial" to eliminate them.

The stronghold of grey squirrels in the Westcountry has led to the extinction of all red squirrels in the area for the last 30 years, but supporters hope they will be re-introduced in the future, particularly in areas where greys have not yet taken over.

In April, the Duke of Cornwall established The Red Squirrel Survival Trust to help fight back against what he described as the "pernicious" grey squirrel. Now, in a recent letter to the CLA's president, Henry Aubrey-Fletcher, he has claimed that greys – introduced to the UK in the 19th century – were doing "immense and increasing damage" to woods across the country.

In order to save the threatened red squirrel and protect efforts to restore native hardwoods and create community forests, a campaign to eliminate greys was needed, he said.

The CLA report is calling for the Government to recognise the importance of woodlands for protecting wildlife, tackling climate change, providing social and health benefits and generating income through pursuits such as shooting.

Sir Henry said the potential for woodland was "enormous and largely unrealised", with falls in new planting and saw mills, low levels of harvesting and very little value of timber returning to woodland owners.

"Meanwhile, forestry and woodlands are over-regulated by Government, and out-of-control deer and grey squirrel populations have caused havoc," he warned.

Mike Seville, forestry and woodland adviser to the CLA, said that 60 per cent of woodlands were currently under-managed and accused the government of a "defeatist policy" towards grey squirrels, which carry a disease that is fatal to red squirrels and do significant damage to trees by stripping their bark, often killing them.

He claimed the "rubbish policy" concentrated on protecting the small pockets of the red squirrel population with buffer zones, which was failing to stop the greys spreading, while millions of pounds of public money had been spent on planting new trees, even though 30 to 40 per cent of them would be damaged by grey squirrels in 20 to 25 years.

Earlier this year, conservation experts from the South West stressed the need to control grey squirrels in the region and limit the damage they did to local wildlife.

Graham Dallyn, head ranger at the Forestry Commission in the South West, claimed they had a "devastating" effect on woodland. "Imagine you have nurtured a tree for 30 years. A squirrel can come along and strip the bark in one morning, and that's it down the drain."

Mr Seville also claimed that, although the Government's policy on controlling deer was much better than its attempts to tackle the squirrel problem, populations of red, roe, muntjac and sika deer were out of control as they had no natural predators, and needed to be managed. Both native and non-native species of deer pose a threat to woodlands by preventing them from growing and damaging plants.

He said: "If we're going to have a population in balance with its environment, we have to manage them, and that means shooting them."