Verified answer

As far as I can see from the Bye-Laws "Starting a fire in a Royal Park is illegal" and this applies to barbecues. I don't even think they allow it with permits.

You are more likely to get away with it if; there aren't many of you, you don't put the BBQ on the grass so that it scorches it and you don't upset others with the smell of smoke.

I know for a fact that you can't barbeque in the Royal Parks (Including Hyde Park) but not sure about the others!

I doubt it as i think everyone will have the same idea. It is a fire hazzard and I think you need a permit