A2? Pfff… Your flight could have boarded from the C gates!
more seriously, what your experience illustrates is how much more adaptable/comprehensive/ efficient it rips handling has always been at airports than with call centres - even the most premium ones (and incidentally as reported elsewhere, quality of support from the ggl line has gone down significantly and become very hit and miss). This superior airport service was true even when ground handling was subcontracted but sadly, for some years, BA stopped enabling airport staff to do that except at its hub, so it’s lucky for you you could discuss things at lhr as from other airports they would have just told you you need to call ba.
other European legacy carriers still all pay their contractors to handle booking and ticketing but ba don’t and to me this has seriously deteriorated my experience with ba.