There are usually several options open to people. Cycle campaigns and regional
CTC peeps tend to organise rides for beginners or those who just wish to pootle.
British Cycling will also usually list the clubs and the levels of fitness required on their website, too. If you're more into the sport side and want to race that might be the other option.
Googling your area and the words "cycle campaign group" or "cycle club" will work. There are time trial clubs and racing clubs, and those that do both.