In a previous job I did plenty of survey flying in the London TMA so it's certainly possible. We applied well in advance to the CAA for a special authority and would phone on the day, normally no problems but got refused sometimes once we turned up. Even that was not normally a problem, there was other work we could go and do and mostly we got what we wanted at some point during the day.
PS. When I say "we" applied, I mean the company, all these years later I have not a clue who they submitted the paperwork to, we were just given copies and a number to call on the day.