This is all getting very heated.
All I can add is that if I were the person being involuntarily downgraded then I would have the following approach:
Firstly I would want to talk to ground staff about why me etc and also compensation and possibility of later flights (with compensation etc).
If I was not happy about the compensation I would then wait until everyone was onboard and then ask to be offloaded (which Long Haul would mean finding my luggage).
I have only played this trick once in my life and it was on an AF not BA flight from LHR. The reason was not involunary downgrading but AF's terrible attitude regarding someone stuck in Cameroon (I can't say any more for medicolegal reasons). I was utterly furious with AF and so I did this terrible deed. I could hear the howls of screaming from AF as suddenly they had to find all my luggage and that there were over 50 connections many of which were tight enough that my deed caused all these people to loose their connections. Yes I did feel teribly sorry for all of them but AF's attitude is the reason that to this day I will NEVER EVER go Air Chance.
Doing this awful deed causes utter mayhem as to then re-open the cargo hold and find your luggage this late causes a huge delay especialy if you are one of the big hubs. It is not to be done lightly and you should have at least argued that whatever you have been offered is not reasonable recompense. If you do this you may also well cause huge inconvenience to up to 355 other passengers etc so I would suspect that once you do this BA would be open to any reasonable suggestion of compensation. Be warned they can call your bluff and just refuse to fly you, though......
Shouting on the plane will not get you anything as the Cabin Crew per se cannot offer you anything. Indeed I would suggest that the crew would be well aware of an invol. downgrade and would make a special effort if you told them quitely and politely.
FWIW for invol. F to J long Haul one way I would expect a 4 figure sum. £200 would feel an insult.
FD