Yes it is possible to fly within a Prohibited Place as I carried out last weekend.
I carried out some filming and stills for a charitable trust based within HMNB Portsmouth. The trust acting as the sponsor completed the relevant paperwork including all of my details and risk assessment to the Base Security Team. Two weeks later the permission was granted with some limitations to the flying area which if truth be told were more generous than we were expecting.
On arrival at site a quick call to the MOD Police control room and also when the task was completed. Absolutely flawless and no issues whatsoever on the day. 