East Cowes Marina have a marquee out the back that come with the BBQ and charcoal. We have used it for club events for several years now, the first time it was blowing old boots and raining, we set the BBQ up on the leeward side and carried on.
For about £75 for the hire it's well worth it.
There is a BBQ area at Buckler's Hard, right by the side of the river at the bottom of the village - prior reservation only. Used to be oil drums cut in half, but now proper BBQs. I think you need to bring your own coals (certainly did when we had a Scuttlebutt rally there are few years ago).
I'm prepared to be told I'm wrong, but the mention of NT in the earlier reference to Osborne Bay is surely wrong. English Heritage? Or were they thinking of inside Newtown?