Snap traps. I know it's not nice, but there are millions of mice in the world and it's the only guaranteed way to get rid of it out of your home.
When I bought some on Amazon the advice said to not touch the trap with your bare hands as they can then smell you on it and avoid it. I used some latex gloves to load it. We caught it the first night.
Find where it's coming out into your house and place the trap with food in it nearby. It'll then go "dum de dum, let me have a little look around here for some food, ooh - look, there's some food right near where I'm walking - yum!" and snap. Seeing your picture, I'd pull off the kick board (they should just clip on and off) and pop it behind it, near the gap.
If you use the non-kill traps I think the advice is that you have to take them a good few miles away as the crow flies as they'll find their way back otherwise. If you're in London, this might be a trek in itself!
Our cat regularly brings in live mice, so we've become quite expert at catching them now, so normally catch and release, but one little bugger was persistent and ended up running around in the kitchen ceiling, so the traps had to be set, as the cats had given up on it by then!
They are bloody brazen things though. I was sat eating dinner the other week and caught a glimpse of movement out my eye. Looked round and there's a bloody mouse trotting across the floor like it owns the place!
Being typical cat owners, we locked it in a room with an outside door, opened the door and went back to eating our dinner! Watched it on a camera and saw it scuttle out the door!
With yours, catch/kill the one you've got then see if another one arrives. If it does, you will have to do more investigating as to where they're getting in, but it IS possible that it's just the one.