My insurer, Legal and General, cover my bike under personal possessions but at nearly £3000 it has to be a specified item. My unspecified limit is £2000, but even it the bike was worth less than this I think I would get it named on the insurance.
As an aside from this, I recently had a bike stolen which has now increased my premium by £200 and several companies wouldn't offer a quotation at all. Apparently after a claim, you loose all of your no claims discount. Not sure how many years constitute full no claims.