If you really want to kill off the mice in your flat yourself, then get a load of the old Little Nipper spring loaded bar mouse traps, five or six of them, and bait them up with chocolate, Club biscuits seem to work best, and leave the traps where you last saw the mouse, where you suspect the wee soul lives, and any other place that seem appropriate.
If you find any mouseholes pour rat poison down them then bung up with wire wool as previously suggested. And if you're feeling strategic, bung up all the mouseholes except one, and leave several mouse traps round that one hole, in a semi-circle.
If the traps kill any mice, use a plastic carrier bag to pick up the mouse and trap and put them in an outside bin with a lid. Get a new trap, bait it up and leave it where the first one was. If you don't catch anything for two months and the mice have all gone, then pack up the traps.
If that doesn't work, move out to a flat that doesn't have mice.
If you want to use humane traps, try leaving a small piles of muesli around your flat. It won't kill them and will probably encourage more mice to take up residence.