I wouldn't be such a soft sod as to dob myself in to the police about it. Not only is it a sign of a terminal nerd, but the fact that it was chucked away means that any theft and resale it's been through was years ago, and it's lived an entire other life since then. That you're feeling guilty that you're the fourth or tenth owner of ten quid's worth of of halfords BSO after it was stolen some time around the release of Forrest Gump is, to be honest, embarrassing. There's newer stolen goods than that in the British museum.

What I would do is get some rust treatment on the ground off serial number sharpish, paint it over, and not worry about it. Maybe you didn't shoplift enough as a teen, who knows.