He has a choice. He has the whole of Europe to move his aircraft to if he'd rather operate in "better" ATC regimes.
As I recall the complaint that Stansted was suffering more than Heathrow was upheld but not because of any favouritism although I believe COVID may have interrupted the follow up inquiry. Now of course the whole world is suffering with ATC staffing issues.
He has to tread carefully so as not to trigger a total review of ATC funding. Currently a 737 leaving a London Airport consumes the same ATC resources as a BA heavyjet but pays less. And a foreign heavyjet overflying consumes very little ATC resource but pays much more.