Thing is, the OP is mentioning a BA transatlantic flight. Now unless he was on the LCY-JFK service, that means the flight took place in a widebody. And onboard those aircraft there's a FA manning every door, and there's plenty of space to get out even if the entire exit row is occupied by immobile passengers.

Things are, as has been pointed out above, quite different when you're in a narrowbody and we're talking overwing exits.