I can't say much other that the operator concerned is a large airline, but is not UK based. I applaud the NATS for their manner in only providing priority to aircraft declaring a Pan or Mayday. There is far too much pressure in some airlines on crews to take minimal fuel even when common sense or local knowledge would suggest the prudent option would be to take increased fuel. It has happened to me in the past, and I know I 'm not the only one, where we've had another aircraft jump the arrival sequence due to a low fuel situation. In effect, these crews have managed to get to their destination on other crews holding fuel.
If the UK procedure of declaring a Pan or Mayday was more widely adopted it would help crews in airlines that fudge fuel issues.