If you have an "Invitation letter" from BA you can take the BA Staff shuttle buses. The BA1 operates from outside arrivals, turn left as you exit, walk past the taxi rank and just go to the end of the line of bus stops and it will stop there. Make sure you get on one going to Hatton Cross and not one going the other direction.
Then get out at Hatton Cross Tube Station and wait at the same bus stop for the BA4 which goes direct to Cranebank!!!!