Proving your keys have been stolen is the first problem most people struggle with when making a claim. I have dealt with one fella who claimed the key fell off his key ring ! He still had all his other keys on the keyring. He had set fire to his car and left the key in the ignition which was recovered and showed no sign of it being worn or damaged allowing it to fall off. He eventually admitted he had lied , but only half way through a Court case.
Burgled homes and keys stolen together and cars stolen with inside men probably makes up less than 5% of total car theft , probably less than that . Alot of car theft is technical theft rather than someone actually creeping up to your car and stealing it. Large majority now are old bangers under £2k due to alot better standard security