I think that the reason for the large restricted zone is to give the authoritys to take approprate action such as intercepting the "lost" aircraft before it gets close enough to leave the authoritys no choice but to have to use force.
All this about missiles is just to seem to be tough on terrorists for the press, just a second or two of thinking about writing the rules of engagment for releasing a SAM into the busy London TMA presents all sorts of problems, if the missile malfunctions you risk bringing down an airliner onto the city and that is without thinking of the risks to people on the ground of bringing down a legitimat target.
Even engaging a light aircraft from a helicopter has risks after all think of the damage a 20mm cannon shell that missed its target could do flying down an East London high street.
This whole issue is about acting early to threats and being able to make an apropriate responce be that to frighten away a "lost" pilot or to destroy a real terror attack over open fields.
All that having beed said I an sure that driving a large van bomb to East London would be a lot more effective and practical than using a light aircraft.