Nobody is saying it out loud because they don’t want the publicity, but one of the many results of the UK’s withdrawal from the EU is that it becomes what’s termed legally as a “Third Country”.
Under EU rules third countries (and the UK will equally see all EU members as third countries but won’t apply the same rules on ownership), cannot own more than 49% of an airline unless the owners are EU citizens.
As a result IAG which is legally based in Madrid, Spain, will own British Airways as the UK government won’t be imposing legal restrictions on foreign ownership. UK citizens will not be be able to own a majority shareholding in any EU-based airline.
Even with a comprehensive agreement on aviation services, the legal status of ownership won’t change.
There’s no question of IAG moving its legal operations to London because that would mean it looses its rights to own Aer Lingus, Vueling, Iberia and Level.
The lead company in IAG remains BA, it was BA who bought Iberia and created the group in the first place. Now its about to become a European owned satellite airline.