Having had the privledge of flying over London many times; it is a magnificent sight. I can wholly understand that every pilot, military, civil, student/first solo? would love to do it. How do you legislate who can and who can't... because sooner of later something will happen; you have to limit it...
I believe the line was drawn at those who one engine cannot and multi-engine can. Equally, a blanket military are OK would cause an uproar amongst the civilian pilots and leave the military at peril should something unfortunate occur (irrespective of how remote you or I consider it to be).
Hence the situation we find ourselves in.
As aside, of my generation of Pilots I can think of 3 who were involved in incidents that resulted in the aircraft being lost whilst in the act of taking-off or landing... 2 Valley and 1 Chiv. Again, no disrepect to the pilots involved or the Hawk.... just a risk of operation......
I am glad to hear that your time with the Hawk has been so incident free.