The Forest of Dean has a popular trail centre with a cafe. There's a blue and red graded trail (Verderer's and Free Miner's) as well as an easy green pootle round the forest. That would be under two hours from Birmingham. Here's the website link
http://www.pedalabikeaway.co.uk/advancedriding.html . And you can read about my experience of it here
http://www.pedelecs.co.uk/forum/threads/so-i-went-to-a-trail-centre.18964/ . You shouldn't have any trouble finding a campsite in the area as a quick Google reveals there to be several.
A bit further a field, but still within three hours is Bike Park Wales
http://www.bikeparkwales.com/ . I haven't been there yet but it's proving very popular and there are buckets of trails there. I have read that the uplift service is so busy it needs to be booked in advance (I've no idea if this is just at peak times or not) but you probably don't need that if you have electrically assistance anyway. As for campsites, I'm not sure as Merthyr isn't the nicest area itself, but you might find some to the north as you head into the Beacons.
Cwmcarn Forest has some trails and is a similar distance but I think they may be closed now for a good while as they have been struck with larch disease (No 1 : the Larch (sorry, couldn't resist)) and sadly have to fell large areas of forest.
Also closed now to my knowledge, but worth considering for the future is combining Cwm Rhaeader with Coed Trallwm (I saw a sign that Cwm Rhaeader would be closed for felling in November but the latter might still be open). Cwm Rhaeader has my favourite red so far and Coed Trallwm has a blue and a red and some very beautiful roads to ride from the car park. Neither has facilities open at the moment. There's a nice campsite at Rhandirmwyn that my parents have stayed at which is very near to the Cwm Rhaeader forest.