I can only imagine that the gate staff advised the dispatcher on the plane that all passengers had been processed through boarding. The dispatcher assumes this meant all were on board and advised the crew of this, so doors were closed. The breakdown in communication must have happened when you all boarded the bus. Headcounts only take place if there is a discrepancy between number checked in to number gone through the boarding gate, so the groundstaff would have had matching figures.
Nonsense - it's the bloke - sorry, person - sitting up front, left hand side, who's ultimately responsible.
Except the Captain is usually busy at this stage and relies on the dispatcher to advise boarding is completed, then the crew to advise doors are closing . What do you really expect the captain to do a headcount themselves???
If head counts are no longer BA policy (is that really true though?),
Yes it is, you try headcounting 300+ passengers on larger aircraft playing musical chairs and darting in and out of toilets!