There has been no ab initio training at Shipdham for years - I don't know if that is going to change now that airfields no longer need to be licensed to offer training (Shipdham is unlicensed)
Although I only know Seething as a visitor I have always found it to be friendly and inviting (and no more cliquey than other places). It is, however, correct that you can't just turn up and learn to fly - the airfield is club-run, and it's part of the deal that one has to spend a certain amount of time helping with the running of the place (serving behind the bar, refuelling aircraft, cleaning the premises, whatever).
Beccles is another option - it's in Suffolk (just) but fairly easy to get to from Norwich.