Obviously it will depend on the time of day that you fly, but remember that Thames Radar are too busy at times to do this. PLAN to join after BIG on track DET-DVR if you want - but don't be surprised if you don't get anything.
Also, don't bother calling SVFR tomorrow - it is the busiest day of Ascot races and the zones are PPR anyway. You will also need to speak to Biggin Hill for clearance through their ATZ and probably only get a FIS from Thames.
There is an element of luck involved really - as if you had asked for that routeing today you would have had no chance for most of the day as Biggin and City were busy. Add in all the extra Battersea movements and you fall way down in the priority stakes.
For Thames to get anyone into CAS they have to ring the Assistant to get a strip, get your plan activated, then ring the en-route sector to get you a climb and integrate if possible into CAS.
Thames only have CAS BIG-DET and North - so you may find it easier to go GWC tomorrow. Especially if you want to get into CAS under a radar service before reaching DVR.
Good luck.