As I recall, and I expect that others will add to it, the Hunter was from 1 Squadron. The story I heard was that pilots were getting fed-up with the government giving the RAF a bad time, scaling it down etc. In a bar somewhere, a pilot (Flt Lt. Alan Pollock if my memory serves me right) who was about to leave the RAF agreed to be elected to fly a Hunter through Tower Bridge as a protest.
It was told to me by a senior officer so I repeat it for what it is worth. I have no doubt if it's wrong we will hear about it.