Currently I'm dealing with ants. I'm with
@LumberJack I don't want to kill anything but when they're literally infesting the house - they're currently using my house as a dumping ground, they dig their ant tunnels then come up through any crack they can find and dump their crap - to keep THEIR nest clean and tidy, so it's also a morgue as they're depositing ant crap and dead ants.... My bait traps seem to keep them at bay!
Good luck with the mice!!
I have dealt with ants a couple times and I found (quite accidentally) that if they come as a swarm, then I kill every single one of them, no survivors, and the bodies get flushed down the toilet. Didn't need any bait or poison, as the baits were doing nothing, anyway! After I found out that this worked, I googled around and I guess I'm not the first one to try it. The theory is that when a huge mass doesn't make it back to the colony, the colony as a whole will mark that entry route as a predator danger and not come back. They happened to invade the bathroom, likely because they were hurting for water more than for food, so a broom and dustpan to sweep them all up and dump in the toilet, flush, and repeat until no more are left. The little buggers are difficult to stomp, and even then it tends to only stun them and they walk away shortly after. So - drowning it is!

Flushing them down the toilet was just to make sure they didn't scramble back out of the toilet before I could get them all in one place.
It may sound cruel to engage in wholesale killing, but the way I see it is that: I didn't use poison to kill the entire colony, and since they didn't come back it was less death for them in the long run. Further, I do not see individual ants as multiple organisms. The colony as a whole is the individual here, and I can explain the rationale if needed. So what I did was to metaphorically bruise the finger of the single organism to train it to leave me alone.
These were the tiny little black sugar ants though, which are about 1.5 MM in length. I believe the ants in England are larger and I do not know if they behave similarly. But if they are tunneling into the dwelling place, I would turn to digging up all the tunnels that they dig in, and if that didn't work find the nest outdoors and dump petrol in there. This is the folk cure for fire ants in Arizona. Who, by the way, are nasty little beasts. Aggressive as wasps, and what they lack in size they more than compensate for in quantity. They crawl up on anything warm, and when enough are assembled, the signal goes out for them to attack at once. Which means you can be minding your own business but standing in the wrong spot, and suddenly your entire leg is in a special kind of pain. This happened to me once. Only once, as there are some lessons I don't have to repeat too many times to figure it out.
Now that I think of it, though, petrol on the ground is probably pretty irresponsible stewardship of the ground water. There might be something equally irritating that is less toxic?