Assuming that you are single engine, there is no route to the LCY overhead that will allow you to glide clear in the event of engine failure. Once you are far enough East to be legal, you may as well just route around the zone. It will take a maximum of 1 minute longer and give you a nice view of the QE2 bridge.
If you have 2 engines, then I believe LCY (is it still called Thames Radar?) are fairly accommodating, traffic permitting.
Incidentally, a VFR flight plan will make no difference in either case as en-route ATC will not be addressed.