Just to echo what's been said - it's the well-fed, much-petted cats who are the best mousers, both because they aren't in a hurry (they can sit and watch a mousehole for hours), they have the leisure to be playful (which, let's face it, is what most mouse-slaughter entails for cats) and also they have a strong desire to please their pet humans with 'treats' - or else to teach them to hunt mice!
I shall never forget my baby son's first Christmas - I was cooking breakfast in the kitchen and my son was on the floor in one of those bouncy-seats - when I looked over and saw that one of our cats, very much the 'senior' one too, had kindly brought my son a half-dead mouse and was trying to interest him in playing with it. I am sure that cat still blames me for the fact that my son remains a rubbish mouser!
Seriously, though, good luck with finding a rescue cat. Given the state of the economy etc I am sure there are a huge number of wonderful cats who would be all too happy to do a bit of mouse-hunting for you.