There was a good suggestion on this thread that ATC and/or the military could have rung up BA Ops and asked them to ACARS the aircraft in question with a frequency to contact. BA 777s have satcom as well, so ground agencies could have made a call, too.
Seems like something that should be set up in the command centres of the various civil/military ATC units. Could save a bit of bother and expense for all.
I don’t know the exact frequency of this kind of incident but I think it’s quite high - possibly several times a day over the whole of European airspace...