Where do you live? Do you know if he is airside/landside? The best thing you can do is either get to LHR by plane or to drive/train and buy the cheapest or a fully-flexible ticket you can cancel (even when airside).
I know it's a bit late now, but you should have requested priority assistance for him - if you do get down to the airport you can request assistance there so he can be taken to the gate when his flight finally leaves.
When you say stuck at the airport, do you mean he was put in a hotel room by BA or slept at the airport terminal?
Finally, don't assume the worse, he could quite easily be sat down somewhere having a coffee and enjoying himself.