Sorry sss but I'm one of those who doesn't even attempt the short cut anymore. It can mean upto 5 internal phone calls to get approval plus the nause of getting the electronics to the eastbound sector-and all to save a few track miles!!
Imagine how it would be if we did this for all the operators eg BMA to NX, MSK to BB.
Also the London Middle Sector was established and one of its' main tasks is to stream the BB/NX inbounds. They could do this very well and then find that you are popping up around BKY.
It really is more trouble than it is worth nowadays,so just take it that unless it is VERY quiet you'll get FL270 via LAM.