BA is not a British airline. Just the wholly owned subsidiary of IAG. For the UK Govt to step in it would have to cease trading and the shareholders would be wiped out. The Govt then creates a newco and purchases the distressed assets from the administrators - if nobody else would do so. Anybody want a knackered 747, an IT system with one careless owner or a 380 unlikely to be full anytime soon? In the long run it could be profitable again and that would certainly arouse private interest at the right price.
Having the ability to get goods and people to key markets is vital to national interest - but BA is not.