I don't think anyone would give permission for this.If one of the homebrews exploded (how likely is that), and took out an eye, the person who controls the picnic area would most likely be responsible.
We had a bbq one year out side the B&C, and had to get insurance for 60,000,000 for one day, in case someone fell off a passing bus and burnt themselves. Basically we had to take full responsibility for anything that could go wrong. The picnic organisers would end up with this resposibility. Sorry to be negative.
And not to compare ICB'ers, to anyone, but if the shit that drinks in public places each day can get away with, why shouldn't we.
I say go for it, but bring a portaloo. Dublin Zoo used to give part of it's area for bbq's and parties. and i have a friend up there. Will give him a shout if you like.