Thanks for all the suggestions.
I checked out all the London lidos. Tooting Bec Lido is fantastic, probably the largest open air pool left in the country. I can only imagine what the cost to hire that for the day would be, but it would probably be at least £1000!
To be honest, I wanted somewhere fairly local. Organising one of these things is tricky enough, whithout having to rattle up and down the motorway aswell.
The small school pool looks nice, but as you said perhaps a little too small. However, very competitive rates of hire. By the looks of their website, the school is based in Oxfordshire.
I've never been to Black Park, however I know it attracts a strong crowd of submariners. One possibility I'll bear in mind.
Birmingham is too far for me. If you want to organise something up there by all means go ahead, and I'll help where I can.
However I couldn't take overall responsibility for the event if it was held that far away.