Spooky2
I retired 2 years ago from BA, but looking at the charts and stand 319 you should call Delivery on 121.975 for start clearance; you will then be told to contact Ground on 121.7 (for that part of Terminal 3) [or 121.85 or 121.9 for other areas] who will issue push clearance.
There is no implied push clearance when cleared to start.
HTH