The airline pilot market is totally international. When I qualified I sent off my CV to every registered airline, corporate operator and air taxi company I could find throughout the world!!! I don't know how many... I didn't count! It took ages. My point is that just because a pilot flies for BA it doesn't mean they are British or trained in the UK. In fact, most young pilots I flew with when I qualified did their commercial training abroad, a lot in the USA.
When it comes to commercial flying with the major airlines we just have to trust that they are all up to the required standard. I can't imagine why a pilot from any one country might be any better or worse than one from another if they are flying for the same airline.
I could imagine BA recruiting from all the major aviation bases around the world.