Time to get some "barn cats"? A mouse doesn't stand a chance around here. I'm all the time finding "gifts" the cats bring me; doesn't matter how well fed they are, they can't resist the creepy crawlies. I get mice, voles, shrews, moles, snakes, frogs, lots of things. I went to St. Louis for a couple of days recently; when I got back there was a nice, juicy field rat at my back door just waiting for me to eat it (I think that's why they bring them to me, gifts to eat.). A cat will catch mice trying to climb up to the GP enclosure.
I would be afraid of a mouse carrying a hantavirus; that's one of the major things that mice transmit to people around here. I don't know if they carry that virus where you live, but I still wouldn't like having them around my pets eating their food.