This may be an off the wall suggestion but I work for BA and they have a whole heap of facilities from their huge Waterside HQ with its own theatre to their various engineering hangars and training centres. I suspect the engineering hangars might be difficult due to the fact they are airside at Heathrow and in a secure area though (and of course they are often in use for fixing aircraft).
However it might be worth talking to them, as a company they tend to be quite community minded and they certainly have a lot of interesting spaces that could be used. Also as this isn't really core business for them they might be a more economic option - after all it's not how they earn their corn. Hosting a bunch of aviation enthusiasts would be good PR.
I will need to try to figure out who to approach internally as it's a huge organisation and I'm not sure whose remit it falls under. If Justflight want to take this forward then just message and let me know.
Birdseed007