Adventure seekers who visit one of Britain’s great wild places are making life more difficult for farmers and putting cattle and sheep in danger, a livestock welfare charity claims.

The chair of the Dartmoor Livestock Protection Society, which was formed in 1963, says the “idle amusement” of millions of visitors is threatening to squeeze out hill farmers.

In her foreword to the society’s annual report, Marion Saunders, its chairwoman, says: “We are concerned that the recreational overuse of Dartmoor is changing the character of the moor and having a detrimental effect on the animals. Off-road cycling, wild camping, marathon running, rock climbing, tobogganing, the tread of thousands of feet, hang gliding and more all occur on Dartmoor and they push hill farming in to the background.”

Almost 2.5 million people visit Dartmoor in Devon every year, bringing £11m to the local economy. But Saunders claimed many visitors saw the moorland farmers as a nuisance.

“Farming becomes an annoying hindrance to the business of more land recreation and in the way of having fun,” she said. “Drivers resent slowing down just because of sheep are on the road, animals get chivvied off the common away from barbecues, tents are pitched where cattle normally walk to cross a river, and gates are left open because the importance of closing them is lost on those with no understanding of farming practices. As soon as snow falls, scores of cars carrying children and toboggans block the roads with drivers oblivious to the fact that farmers have work to do and fodder to transport.”

Visitors explore Dartmoor’s Haytor Rocks. Photograph: Alamy

But she said that outdoor activities would vanish if there were no farmers on the moor. “If hill farming is getting in the way of leisure pursuits on Dartmoor, conversely an absence of grazing animals would put an end to almost all outdoor leisure activities. Dartmoor would become an overgrown and impenetrable wilderness.”

She quoted a letter Beatrix Potter wrote to the Times about a plan to fly seaplanes for visitors in Lake District. The author wrote: “I respectfully maintain that work, business and undisturbed customary use of centuries should be set before idle amusement.”

Saunders, who is a farmer, said: “Similarly here on Dartmoor the idle amusement of millions of visitors should not be favoured over traditional farming practices, nor be allowed to jeopardise the welfare of the livestock rightfully grazing the common land.”

By law Dartmoor National Park authority is obliged to conserve and enhance the natural beauty, wildlife and cultural heritage of the national park, and promote opportunities for the “understanding and enjoyment of the special qualities of the [park] by the public”. The authority says it has eight objectives, the first of which is “to maintain a viable farming community that delivers a range of public benefits”.

The authority’s website promotes many of the activities Saunders is worried about, including cycling, wild camping and climbing, as well as ones she did not highlight, including canoeing and letter-boxing, a pastime that originated on Dartmoor and which combines orienteering with hunting treasure and solving puzzles.

The authority’s chief executive, Kevin Bishop, said the problems faced by farmers were caused by a minority. “Our shared challenge is to influence the behaviour of these people so they understand their role in caring for this special place. Our national parks were designated by the nation for the nation to balance conservation communities and enjoyment. As an authority we are supporting the farming community and providing opportunities for people to enjoy and understand the national park.”