Rural campaign groups in Devon and Cornwall are lobbying the new government to change liability rules about livestock.
The Animal Act 1971 means owners of livestock are legally responsible for any damage caused by their animals.
But owners say they should not be liable if they have done everything they can to prevent an accident.
The government said it would be "clarifying the Animal Act 1971".
In 1971 the act made owners of animals such as lions and tigers liable for any harm or damage caused by them.
But in 2003 this was extended to livestock, following a road accident in Devon in which a horse escaped its field and collided with a car.
The driver sued under the act and the House of Lords ruled that the owners were liable even though they had fenced their field.
The regional branch of the Country Land and Business Association (CLA) in Devon and Cornwall wants the government to reclassify the law.
John Mortimer said: "If you're not negligent, you should be protected, but it shouldn't be strict liability and unlimited consequences."
Graham Goddard of Dartmoor Hill Pony Association said: "Most farmers would have public liability insurance, but does that mean we're obligated to cover the public when they're walking across a public footpath?
"How do we ensure out animals don't do anything to injure them?"
In statement, the government said: "Defra remains committed to clarifying the Animals Act 1971 and we will be working the CLA and other organisations to achieve this."