Velodromes
Track racing is booming in the UK at the moment especially indoors. Tracks like Manchester Velodrome, Calshot, Newport and very shortly London not only put on races in the form of either a league or one off event. They also have regular training sessions for all ages and abilities. Most tracks have hire bikes so you don't need to go out a buy a bike. You can book a taster session to see if you like it.
Once you've done the taster session, followed by an acreditation you can start to book yourself on training sessions.