Sorry if this is labouring a point but I see it appear in forum after forum, hardly a week goes by without someone saying.
"I think BA as the national flag-carrier ..."
They are a publicly owned company, listed on the stock exchange. They are not owned by the UK government, so they are not the national flag carrier. Whether they have little flags painted on the side of the aircraft is inconsequential and only a matter of P.R. and dewey eyed folk on airline boards.
BA are the largest UK airline but nothing more or less than that.
OK, as you were.