The classic terrier headshake will most certainly kill rabbits in a trice. My lurcher / terrier cross despatches mixie rabbits this way. Bit of a bogger getting the carcass off him though – he likes to prance about, proudly displaying his prize for the next half hour, past all the shocked looking old dears with their pampered Westies and handbag dogs 😳
Seems a shame to spoil his glory by taking it off him…
EDIT; after a quick re-read of the OP, just make sure you're able to recall him when you don't want him to chase sheep / other dogs / rabbits crossing motorways etc. I did this over the course of a month using a hard rubber ball. Got fed up of him tearing off after other dogs, no matter how far away they were or what was between them.
I'd throw the ball and alternate between calling him back mid-chase and letting him 'follow through'. He got rewarded for abandoning the chase on command and totally ignored for failing to do so. A bag full of chopped up sandwich ham works wonders but it does take time and a massive amount of patience.
EDIT #2; ….and if you can do that with a lurcher, you can do it with any dog – their recall is notoriously bad and he's absolutely obedient now – almost 100%.