FL90 is the notified minimum overflying level in the London TMA, however, on the day if things aren't too tricky we may say yes to lower.
The problem with FL70, especially when you get to between WCO and BKY/CAM is that you're in the teeth of everything. All out outbounds from SS on BUZAD and CPT SID's are transferred to NW Deps on a standing agreement at FL70 when the pressure is high (1013mb+) and FL80 when the pressure is low.
Another thing, if the pressure is low, FL70 isn't separated from 6000ft and the LL WOBUN/BUZAD SID's climb to 6000ft as does the GW OLNEY SID on Rwy 08 and LC BPK and CPT departures are usually coordinated in at 6000ft.
So, as you can see, at those levels you are in the middle of absolutely everything. If it is remotely busy at all you can expect to get told to drop out the bottom if you can't take a higher level or end up getting vectored around the sky. I'll do my best to accommodate you but if the traffic situation is complex (and believe me, it can become VERY complex in that bit of airspace) I'd have to turn you away.
You're more likely to be accepted if you elected to route up towards the DTY direction but I honestly don't know how that would work out from a flight planning point of view.