It's an interesting situation. The problem Virgin have is that the British public now see him as public enemy
#1 after demanding billions on day 1, and MP's calling him out in the house of commons to pay his staff with a small percentage of interest on his fortune. Branson hiding on his island and not paying UK taxes doesn't exactly help him, and the FlyBe debacle didn't play into his hands exactly, Plus a lot of people on both leave and remain sides resented someone living on an island and tax dodging poking his oar in telling people how to vote. I don't see Rishi Sunak being willing to bail him out at all. Politically, at this moment in time he'd take the populist stance and let Virgin go under. Yes, I know most of the planes aren't his and most of the cash is tied up elsewhere, but that's not how the British public see it. The only way Virgin will survive with the government being lender of last resort is the UK government pretty much owning Virgin, and selling it off at a later date once the monies lent have been repaid. It's by now quite clear that of the two options, politically the government would choose let them fail.
BA - well, it's not a British company any longer so why would they even discuss state aid? Although it is possible that the government might take the whole lot off of IAG and bring it back to being state owned - maybe.
But in either case I don't think the UK government have them as as a priority, and any aid they do get the airlines will pretty much have to pay for in blood.