First, I'm in the U.S., so my opinion may not be worth as much to you as someone from the U.K. But, I've purchased a number of tires through the internet. As Maz1 said, it's definitely to your advantage to confirm the size needed by checking the sidewall of your current tires.
My comment/warning is to be sure that you have a garage/tire dealer who is willing to mount and balance tires that you've purchased somewhere else... and at a reasonable price. I'm lucky in that I have an excellent relationship with a local independent tire dealer. I have several vehicles, and my deal with him is that I'm free to source tires from the internet if I like and he will mount and balance them for me at a fixed (and very competitive) price. If he can obtain the same tires from one of his suppliers and can match the internet's price, I'll buy them from him, instead.
Second, if you have alloy rims - or any that are of a special or unique construction - make sure in advance that the tire shop you've chosen has the equipment to mount and balance them. I compete in some amateur motorsports and can tell you, for example, that not every shop has equipment capable of mounting rally tires (because of their extremely stiff sidewalls). Large diameter wheels may precipitate the same type of problem.
Final comment: F1 tires. The current supplier is Pirelli and the reason they produce six types of tires for those cars is because that's what the FIA asked for. There are 'hard', 'medium', 'soft' and 'super-soft' types; as well as two types of rain tires, one type for light rain and one for heavy rain. In their constant twiddling to try to make the races more interesting, the FIA requires that Pirelli bring two of the four types of 'dry' tires to each race. The types brought are dependent on the track. Each competitor must use at least one set of each type of dry tire. This rule is intended to force each team to make at least one pit stop during each race. At least in theory, it also levels the playing field a bit by forcing the teams to compromise their 'set-ups' to accommodate both types of tires. If it rains, this rule is suspended.