To the best of my knowledge jet aircraft with afterburners are not allowed on the UK civil register. This affects many other ex-military aircraft & not only the Lightning.
I think it's more to do with the catogorisation of aircraft - the Lightning, like the Buccaneer, Vulcan and Sea Vixen is listed as a complex type. This opens a whole can of worms - manufacturer support (and liability in event of an accident?), aircrew qualifications and currency, how the aircraft can safely be operated in UK airspace and maintained as a civil aircraft and lots of money. Then lots of money to convince the CAA that all is well. And airframe life of course. Then there's the safety record from its service in the RAF - not the best, particularly with regards to engines giving up the ghost. They're probably quite nervous about the noise problems too.
All of these have been major hurdles for the Vulcan - for example I believe the CAA have stipulated that all the aircrew have passed the RAF's Vulcan OCU (quite a large hurdle). Marshalls have taken the engineering support - I think also for a complex aircraft the engineering support cannot be volunteer labour.
Much as the CAA are given a lot of flak, it must be remembered they administer some of the busiest airspace over a relatively small area, and some aircraft types are probably safest on the ground.
