Not sure who is best to help you hear as this is a nightmare, Daisy my terrier when she was a baby was dreadful for chasing anything and tbh I for 2 years could not safely let her off the lead. She once set off in chase of a deer and was miles away, all we could see was a white spot in hot persuit of a Roe Buck

and she would NOT come back. I have worked with Daisy over the years because I have had to because she was going to either end up ketting badly injured or worse shot for her chasing skills. She once dissapeared for hours and I was terrified that she had met her end, only to find her back waiting at the house
Daisy's cure was Balls and sticks, she became so obssessed with them that they keep her attention on our off lead walks, although I would not trust her 100% and because I know the ground here I will put her on the lead in parts I know there potentaily could be deer or hares. Daisy can pick up the scent of a deer or hare in a flash (she is not bothered about pheasants as there is no chase factor in them they are for daft gun dogs to play with )

so I have to be switched on and on her case the minit I see her mood change. Im not going to tempt fate by saying she has never chased anything for a while but touch wood I have managed to find out just how her brain is wired in that area

I would deff get help as it is indeed illegal for your dog to chase deer and to be so called hunting out of control, although no one goes out with the intention to let their dog chase/hunt , but if you know your dog had this problem then you are indeed carrying out an illegal act.

Teaching them not to chase: well there are various different methods taught by a range of trainers and its really up to you as to which suits you and your dogs. I hope you get it sorted

Edited to ask: which area are you in
