I don't know how it is in the UK, but here in America, the police won't pay attention to one piece of stolen electronics.
My very close friend and his other roommate went on a bachelor party vacation only to find that all their belongings (PS3, laptops, televeison, etc) were all stolen. Their third roommate curiously had nothing stolen. Then they found security footage of him carrying out all the electronics to pawn. The police did nothing. In, fact, they ended up having to have home owners insurance paid out.
A place where I lived for five years had a mail thief. He would routinely break into our building, steal all our packages and mail, and have yard sales of all our stuff. He successfully thefted the identity of several of my neighbors in the building. He'd follow the post man on his route and brazenly break into people's mail boxes and shove everything into his white conversion van he used to tail the postman. We all knew who he was, there was footage of him in several buildings in the area of him stealing mail. Eventually, we had a neighborhood meeting at the local police station with he PD and a USPS's federal investigator. Even though we collectively had had thousands and thousands of dollars of mail stolen, credit cards fraudulently opened up in our name and used, and he even brought in a neighborhood drug dealing problem; the federal investigator told us they wouldn't be taking on the investigation. The police liaison added insult to injury saying we should feel lucky we didn't have more people like the mail theif in our neighborhood, and told us to stay safe.