However, the chap who has the stalking in the woods says the deer belong to him and I am not allowed to shoot them. Surely that can’t be right?

Wild deer are just that, wild, and only belong to someone when they have been ‘reduced into possession’ by being killed.

They then belong to the owner of the land on which they were killed, regardless of who actually killed them; though the landowner may, of course, have a venison sharing agreement with whoever carries out control measures for him.

You are therefore quite free to shoot marauding deer for your farmer if he wants you to, subject to any legal requirements such as close seasons, permitted firearms etc.

It may be that under the circumstances you describe it may be lawful to shoot the deer during the close season and also to use a smooth-bore gun and cartridges with the required size of shot (AAA or a slug in England and Wales).

It is too big a subject for a short answer so I would recommend reading the excellent book, Deer: Law and Liabilities by Charlie Parkes and John Thornley, published by Swan Hill Press.

If your neighbour doesn’t like the Law, you might gently suggest he fence his wood so the deer can’t get on to your ground. That would save everyone a lot of trouble.