In message , at 13:35:22 on Thu, 16 Jun
2016, tim... remarked:
If all fares originating in the UK go up, then competitively it's still
a level playing field for the airlines

Not quite. Airlines that rely heavily on UK hubs will lose out to those
that use non-UK hubs, as more passengers will choose to change in Paris
or Frankfurt instead of London.

but just what is this underlying reason that will make (BA) fares go up
in the first place

All-round worse deals for the UK as: an EU outsider flying to the EU;
and [separately, remember] with less bargaining power for destinations
outside the EU.
--
Roland Perry