Arriving at 2pm, with last check in at 3:15 and a terminal change is probably cutting it a bit fine, especially if you need wheelchair assistance. T5 is a long way from T1. You say that not having enough time was not the reason they didn't put you on the flight. What do you think the reason was?
In any event, there is no excuse for treating you badly however. In terms of putting you on the next available flight, it sounds like BA did the right thing, but communications is not their strong point....there are endless complaints trying to get BA to give people a straight answer.
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