This article on an anti-Brexit webpage has an interesting interpretation of the catch-22 situation
If UK airlines want to fly within the EU they need to be 51% EU-owned.
For UK airlines to continue enjoying the same access to the US as they currently do under the EU-US Open Skies, they need to be 51% UK-owned.
Unless someone can come up with a way of an airline being 102% owned by both UK and EU entities (I've tried several times, even my terrible maths can't make it work), I'm guessing the simplest solution is to split BA (or IAG?) into two airlines: British Airways (UK) and British Airways (EU).