BA allows 1 bag+laptop/briefcase. Its BAA who does not.
Boarding Pass is correct.

Options
1) Put laptop/briefcase in bag if there is room
2) Have a large Selfridges carrier bag that can fit both you main cabin bag and laptop/briefcase - you only need it for the security area. You can pack it away after the security scanning machine area.
3) Acquire a laptop/briefcase at duty free before boarding
4) Locate another pax without any hand-luggage to walk through with you (?)
- maybe dodgy for other reasons