I agree with you that it is far from obvious. Perhaps a rather strenuous case can be made that buying an air ticket which includes a right to enter premises where alcohol is served can be assimilated to a licensable sale within the meaning of the Licensing Act 2003, in a similar way that you could not escape the Act by merely charging a fixed fee on entry to a pub and a 'free bar' inside?

I also wonder whether there is anything in aviation-specific legislation/carrier-licensing/airport regulation, etc...?

Thirdly, even if there is nothing in there, BA could have that in its regulations and it would be a fairly sensible type of regulation to have for a responsible carrier.