From Natural England:
By law, you must control your dog so that it does not disturb or scare farm animals or wildlife. On most areas of open country and common land, known as ‘access land’ you must keep your dog on a short lead between 1 March and 31 July, and all year round near farm animals.
You do not have to put your dog on a lead on public paths, as long as it is under close control. But as a general rule, keep your dog on a lead if you cannot rely on its obedience. By law, farmers are entitled to destroy a dog that injures or worries their animals.