gates are often only allocated when the inbound aircraft is taxiing to T5

if they inbound is late then the gate may well be shown later than anticipated.

if the turnaround time is 45 minutes then it can be 45 minutes before the gate is know. check in staff, and the team checking access to the lounge can often see a tentative gate and will inform you of that, but if the aircraft at that gate is late pushing back you could be moved

also, they want you to go shopping rather than sit at a gate, which I suspect also contributes to the "gate shown at ..."

BA778 is being serviced by G-DBCA which landed from Dublin at 11:00 BST (10 minutes late), so I assume you will leave from gate 23 and it should be displayed by now??