Hi there.
The Gloucester Group is close to you and very active
http://www.trfglos.org.uk/There are also at least two groups in the Bristol Area.
A good starting-point is to buy the Ordnance Survey maps for your area and look for the Byways Open to All Traffic +++++++ in red or green, depending upon map scale.
Unless there is specific official signage on the ground indicating otherwise, these routes are all legal to ride for road-legal riders on road-legal bikes.
There are loads more legal routes in and around Gloucestershire, but it's best to seek advise from the local group about these.
The Gloucester Group also gets occasional access to some interesting areas in its role marking out horse endurance events ... like Cirencester Park for instance. If you go along to a Gloucester meeting you can find out more.