IFR in the London TMA is always a bit hit or miss... Sometimes you have to hold and wait 20+mins to get through.
It is quite unlikely that you'll get across Gatwick at 6000ft (or probably any height above the usual VFR transit at 1000ft crossing perpendicular to the runway), your IFR route probably would be something like Popham - GOXUL to join L9 then out to KONAN which is probably a similar extension to your routing south of Gatwick. Albeit perhaps an easier route as IFR in CAS is much easier than IFR OCAS (at least in my mind...)!