I am always at the gate according to my boarding pass. Even if I have to wait and am in Group 1. But I am risk averse in these matters.
I do find LHR a little bit dodgy if I am sitting in GF and my flight is in Terminal C, I get a little twitchy.
I think BA's handling of the case is not good enough, which is no suprise of course.
I cannot help with flight movements but personally would put it down to a harsh lesson learned and move on.