Most of the airlines I fly with do a headcount.
That piece of information has made me more reluctant to fly with UK carriers.
Talking here as a BA 744 driver:
In the olden days of the Classic 747, and the days of headcounts, you could be there a week trying to get the count correct. Each time it was done you would get a different result. 500 passengers and it would be, 499, 503, 498, 512, 489, 499, 500.. yay we can go. Hopeless.
Now the BP has an electronic tag that is read by the machine at the door. That is how the heads are counted in this day and age. So when we are "one down" we know exactly who it is, we know exactly (ish) where on the aircraft his bag is, and we can get that bag off quickly, and get on our way.