I've googled, but why can't these planes fly?
There are, to be fair, a few design issues with the Lightning. The control elements pass between the engines, as do the hydraulic lines.
I understand that one of the biggest issues is that the Lightning, unlike a large number of aircraft, has no manual back-up control measures if the hydraulics fail. With no physical linkage to the control surfaces, if the hydralics fail you end up with an uncontrollable semi-supersonic missile. The CAA are understandably a little nervous at allowing such a proposition to fly in a crowded area like an airshow......