Very true @MEL_Traveller. The issue would move from whether it was technically or legally feasible to in fact whether it was something that would be economically, politically, or commercially desirable. There would be significant arguments going back and forth; from investors, institutional and governmental stakeholders, competition and protectionism issues (particularly in domestic markets or in markets where margins are already tight and the loss of consumer traffic/cost has viability concerns) to the ultimate consumer benefit and what cost/price an organisation is willing to pay to match it.But consider it from the other angle... if I'm a shareholder with BA (or Lufthansa or anyone of the other airline groups), or a government providing support to my national airline... why am I going to let foreign airlines take money simply to allow their members access to some lounge? Unlikely to happen.
The UK may be looking to establish trade agreements, but they also work in reverse. If the UK was to allow every airline in the world to fly ex UK to anywhere else, other countries would take reciprocal measures. Not something BA/VS would want. Nor would Qantas like to be forced into having open competition from NZ/SQ/CX/JL in the Aussie domestic market.
I suspect the risk appetite is low at present for any significant changes to the current arrangements, particularly with demand so weak and given the wide range of fiscal and commercial challenges in the sector at present.
I sit and ponder further....