It's in their nature I'm afraid. My dog has caught two rabbits killed one. Killed a couple of birds and injured countless mice. All you can do is keep an eye on your dog as much as you can but I don't think you can stop it completely unless you keep your dog on lead all the time.
I’ve just spent three years educating Coral not to chase and not to catch.
She once caught a chaffinch and brought it to hand completely unharmed- it flew off when released though I don't hold out much hope it survived due shock. She’s never killed. Training was stepped up as even once is unacceptable to me.
It can be trained but takes patience and the help of a gundog trainer.
To quote Peter Jones - “we ask a lot of our dogs: they are born to hunt, flush, chase, kill and eat their prey. Our job is to interrupt their natural cycle and ask them to retrieve after the flush...not all dogs can do that and not all handlers can train their dog to do it”. I think he may have been referring to Coral at the time