while I don't fly for BA, my airline does a head count, and compares it to a ticket count/boarding pass count and we get those numbers from the flight attendants. this should allay the fears if an evacuation happens.
however, the FA head count is compared to the gate agents ticket count and must be reconciled before takeoff.
we have taken off with ''the numbers'' only to get new numbers three minutes after takeoff.
so, naturally we return for landing and takeoff with the right numbers (kidding of course!)
but it is important to get the right numbers, even after the fact to calculate landing weight and Vref.
and if you are delayed by some company like BA, be smart and request an alternate taxi route so you can get to the runway, even by back taxi.
Smart pilots like to leave extra room behind other planes in case of problems, either numbers or mx so they can keep going via another route.