If you are routeing via DVR, I would suggest you file via BIG, remaining outside CAS. Work LL SVFR and then say you want to work Thames Radar and request a joining clearance for CAS after BIG. If you request to join before this, it may well be refused as the TMA is so busy.(LL , SVFR and Thames Radar sit next to each other at LTCC, West Drayton).
Hope it works, enjoy your flight.