Hi Martin,
I used to ground handle in Windsor Great Park, in the dedicated kite flying area, but was asked to pack up and leave by the park rangers. There wasn't another living soul anywhere near me but they just didn't like it for some reason. I've since contacted the main office to ask for clarification, just in case they were being over zealous on that particular day, but I just got a flat NO.
Someone did suggest Upton Park in Slough as a likely site for a bit of practice but I never got around to checking it out.
It might be worth your while having a chat with Simon with a view to visiting Membury. I'm not sure what the rules are on visiting at the moment but it would be a quick blast up the M4 for you if he gave you the thumbs up.