The Thames Radar area of responsibility for VFR flights is within the M25 and East of a line drawn North - South through Battersea heliport, but excluding a 10 nm radius of Biggin Hill. That having been said, there is always an overlap between the areas covered by different ATC Units. The furthest North East I personally would give a service is Chelmsford, and the furthest South East is Detling. Thames is not a LARS Unit so you will probably only get a FIS from us routinely, although RIS might be offered occasionally subject to workload. By all means give us a call when transiting between LAM and DET, but be sensible about it - if it is in the middle of the morning or evening rush, then just listen on the frequency.
My suggestions are:-
1. When transiting any ATZ call them 5 nm before for traffic information and clearance through, e.g. EGSG and EGTO.
2. Brentwood/Chelmsford area heading East or North East - Essex Radar.
3. Tilbury heading east - Southend.
4. LAM - DET and South of the Thames heading SSE - Rochester.
5. North of Rochester heading East towards Chatham - Manston.
6. South of DET heading South - Headcorn.
7. South East of DET heading South East - Lydd.
8. LAM - BPK - Luton, but only if you wish to transit their airspace as they are no longer a LARS Unit as you know.
9. Anywhere else London FIR 124.6.
Having said all this, if at any time you are in an emergency or unsure of your position, immediately contact any of the radar units in the general area. Thames or Essex are probably best as Southend has no SSR.
Just a few ideas. Hopefully others will contribute.