That's not correct, White Cable operates independently on the Isle of White and you also have Smallworld Media for more Northern parts of the country, while Virgin Media fills in the rest. However, these are all quite isolationist networks that usually require you to have a phone line with the broadband.
The problem is that you won’t have a choice, they only cover specific areas of the country and do not compete directly in the same areas with one another. Not that I know of anyway.