Simplest form of racing is Time Trailing (TT)
. The club runs a series of TT's on Tuesday evenings throughout the summer, where you can just turn up and give it a go. Road racing is a little different, they usually require you to me a member of a racing organisation (BC, TLI, LVRC) and to be fairly confident at riding in a group. If you chat to an experienced club member, they can point you in the right direction.