In the last two days, this has happened to two people I know!
My aunt and uncle have been getting mail addressed to someone with their last name at their address about various bank loans, etc. They finally went to the police about it yesterday after getting nowhere at the bank, and the police are looking into it as serious identity theft!!
Then this morning, my BF called me to say that he'd had a phone call from his credit card company regarding unusual activity on his account. Apparently, someone charged £3,500 to an online gambling site to his card!