There are several options.
1. Get your landlord or lady to deal with it. If they care about their property they will be onto it pronto!
2. Get a cat. A couple of friends have offered to lend me theirs but the responsibility of taking care of them well, let's just say I value my friends and the fact they still value me.
3. Get a trap. You have to decide what to put on the trap, cheese or chocolate. You have to wonder if mice have wised up it over the years. You have to handle them. With a gloved hand or a plastic bag but you still have to handle them. Not a problem for the non-squeamish.
4. Get poison. The thing with poison is you don't know if they will eat it. You don't know where they will go off to die. You don't know if it will work.
5. Get glue pads. Man in the DIY store said he swore by these. Had caught over 20 mice with them over the last month or so (20? Hear me weep...). The mice come out of their cracks and get stuck. "They can stay on there for ages," said the man. He said what you should do is when you've captured one, put the mouse on pad in a plastic bag, then bash it against a wall to kill it.
You may have the stomach for that. I'm not sure I do.
6. Get an Advanced Rat and Mouse Repeller. About £25. You can get a battery operated sonic one for half the price. Apparently they emit a high pitched squeal too high for any animal but a rodent to hear. Pal on facebook gave me that tip. I ran there for support last night.
7. Live in a Tower, preferably quite high up. The higher the better in fact. I'm not sure mice like lifts and they certainly don't like clambering up hundreds of deep concrete steps. Not in my experience anyway. Possibly only perk to living in a Tower unless you have a fantastic view.
lots of luck
I wish you lots