The only good use for a ‘humane’ box type trap is if you trap mice in it then chuck it in a drum of water and drown them. If you release them, even a fair distance away, they’ll keep coming back. Best to just kill them instantly, drowning isn’t a terribly nice death for them, if effective.
Get little nipper mouse traps, they’re ace, you can set them really finely, takes hardly a mouse paw to set them off, powerful too. Bait with some sort of chocolate bar that contains caramel, twix is my current favourite, the caramel helps stick the bait to the pin on the trap.
I’d also chuck some poison sachets under the floor, but would advise caution on that if you have mice catching cats in the area (though evidence to date would suggest otherwise.
I know I seem pretty bloodthirsty, but not being able to sleep for weeks because of mice in the loft making a noise all night kind of drives the humane approach out of you. However DO NOT under any circumstances use glue traps, they’re horrendous.