Rodents (especially rats, but to an extent mice) are neophobic. That means they're very wary indeed of new objects. With this in mind, you'll need:
Spring loaded traps (vary number according to the size of your place, 2 a room is OK)
Poison bait stations (Rentakill or The Big Cheese etc)
Chunky peanut butter and/or Nuttella (cheese is a myth, but rodents go mad for these!)
Bait the traps with a generous dollop of peanut butter/Nuttella and set along skirting, close to the wall and preferably behind objects (wardrobe, fridge, cooker, washer etc) where you've seen rodent activity. Put the baited end closest to the wall. Set bait stations in similar locations for maximum effect, but don't place a trap AND a bait station in the exact same space.
Remove ALL food sources from the floors (unsealed bins, bags of dog/cat/animal food, etc). Then, survey the OUTSIDE of your property - they're getting in somewhere. Any hole big enough to fit a biro in is big enough for mice to enter. Buy a roll of weldmesh/fly screen and a can of expanding foam. Stuff a piece of mesh just bigger than the hole into each one to make a tight fit, then fill the hole with enough foam to slightly over-fill it. Double check around pipe entrances, gas meters, phone/sky/aerial cables etc. Make sure you close ALL holes.
The rodents are now trapped in your house with no escape. They will be forced to seek food and water inside your home rather than being free to enter and leave at will. The only food and water supply they'll have is the traps and bait stations.
Wait.
DO NOT disturb any traps or touch bait stations once they're laid. They'll need to be left to become part of the 'fixtures and fittings' before rodents will consider going near them. If they are disturbed regularly they'll have a 'new' scent about them and stink of human (which you don't want!). Only touch a trap if it's caught a mouse, in which case bin it and set another, or (if reusable) release the rodent into a bag and bin it before relaying the trap.
Good luck.
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