I had my first experience of wheelchair assistance not long ago after a traffic accident on a trip. A real eye opener, though broadly positive experiences at various airports (due to complex itinerary). As other have said, there are different approaches at different airports. My biggest concern was whether the wheelchair assistance (which was not on original booking- obviously) had been noted on the booking- and in each case to my surprise (I generally expect the worst these days) it had been. So, yes, at the check in desk I was usually directed to sit down (cue hopping//shuffling with crutches) and then someone would pick you up, take you through security and right up to the gate. Then I hopped down the a/c aisle which I was able to do.

I have never departed LHR needing wheelchair assistance, but I arrived back in blighty at T5 and to my surprise the wheelchair was already there and waiting, and everything ran smoothly. I had to suspend my usual urges of speeding through security, getting off quickly etc. everything just takes much much longer (stating the obvious).