It is brandable for Classic - could even have a second-hand car dealer character "Classic Al".
But using it for Classical music makes more sense.
Worth noting that the most natural two word competitor classicalmusic.co.uk redirects through to Classic FM's .com site, so there's no risk of confusion.
It's a very strong name, but building a site to match (given the massive range of classical music) is near impossible. Personally, I'd buy a couple of Classical Music magazines, and look for companies advertising in there that have a decent site but a daft web address.