This is not correct. There is no law on the books in the UK which compels ISPs to filter content. There are a couple of court orders in place on some larger ISPs to block access to a few sites, however.
However it might as well be. According to https://en.wikipedia.org/wiki/Internet_Watch_Foundation#Blac... it is in effect on 90%+ of UK ISPs and there is significant pressure on ISPs to implement this technology.