I read that a bounty may be reintroduced for grey squirrels. If you can train your cat to stick to them, and bring them back for you, you could be on a nice earner.
I don't feel mice & rats are much of an issue, either. He's doing a good job for you. I don't think mice & rats will ever become an endangered species, no matter how many cats there are.
I don't like it when they kill birds though, as it seems so many species are struggling under pressure from environmental issues already.
There isn't much you can do to stop him, it's just natural. Even cats with bells can catch things, though it does give the prey a fraction of a second's more warning. As someone said, if it gets to you, don't have a cat.