Hi, we had a masive problem during the summer, it turned out that they were coming in through the same gap that the cold water pipe was coming in the kitchen, the gap was tiny but big enough. Apparently one of the only things the little bugger cannot chew through is wire wool, (plumbers merchant or diy shops )fill the gaps up with wire wool. we filled all the gaps with wire wool, put traps down to catch the ones that were already in the house and over a period of a few days, problem solved, we found that traditional rat/mouse traps the best and the buggers prefered peanut butter with nuts, not the smooth stuff !! As for the cat idea, at the time we were having about 10 mice/rats a day, all in the kitchen where our FOUR CATS ALL LIVE !!non of the cats caught even one !!
hope that helps