We live in NE Bristol and can't think of 1 commercial campsite in the area NW of Bristol, there may be something in the Almondsbury, Thornbury or Chipping Sodbury areas and there is a nice campsite further afield at Slimbridge.
The best bet would be one of the sites on the A38 or A370 south of Bristol or you might find a CL with hook up in the area you are talking about.