We had a bad rat and mouse problem before moving into our place in dulwich. We got a cat and thank god it is a hunter, thousands of years of hunting skills so now there are no sign of mice or rats. She would often just sit out in our garden for hours where the mice use to come from waiting to pounce, and once she catches them she eats them in whole so no need for disposal. The ancient Egyptians use cats exactly for this reason - to catch rodents and prevent disease which was why they were worshiped as gods because they saved peoples lives!