So, there are a couple of ways I can see implementation of these programs going:
(1) If UK-based programs are taxed/axed, I think there's a good chance you can just put a fork in BA 'cause they're done (since if non-UK programs can continue operating, there would immediately be a massive disadvantage to BA vs AA, for example). Of course, IAG being registered in Madrid would probably just result in them ducking out the back and saying "Whoops, this is an EU-based program, not a UK-based program, sod off", which would put them on better footing than VS.
(2) I can't really see the British government succeeding in banning FFP earnings on international flights to/from the UK on non-UK airlines, but I think there is a very strong case that if they tried that, the main effect would be to make the third Heathrow runway a pointless exercise (since however thin the earnings might be, you're effectively hiking the price of those tickets by 5-15% in most cases, something that would probably stack with UK APD in a very...unpleasant...way). I would expect to see a decent amount of traffic shift to Paris and Brussels (in particular), especially if you hit through-tickets as well. At least this wouldn't hose BA directly.

I do think that one thing would help both cut emissions and potentially help consumers would be to restrict up-charging direct flights vs out-of-the-way connections. On the one hand, if the stop is mostly "on the way" it isn't a big deal, but there's something silly about being routed 500 miles out of the way because, hey, hub-and-spoke!