To an extent, yes, but it's also in part down to the baggage fees encouraging people to take carry-on luggage at the size limit, meaning if you're not in the first half on board, you may end up with it under the seat in front, which I'd extremely uncomfortable if you're tall.
But it's also the layout of the airport and the high gate utilisation, and fast turnarounds. It can take 10-15 minutes to the furthest gates, with queues for other gates often blocking your path. But they won't post the number until the previous flight has departed, which may not be very long before your boarding time.
As regards BA charging for food - mainline BA didn't, but BA Connect (the bit that was eventually sold to flymaybe) did. But not at London City because bankers.