Interesting choice of examples IMO.
The US version of The Office is apparently by far the most watched show on Netflix (US). Even if you acknowledge it went on probably one or two seasons too long (which isn't an uncommon opinion, to be fair), 7 seasons is far longer than most BBC shows last.
And, as another poster noted, I would argue that a lot of people think the BBC version of Sherlock has definitely gone on way too long.
I think British TV has actually started taking influence from American TV over the past decade or so (or at least realized that Americans are watching and have started to cater to those audiences). Downton Abbey I feel also similarly went on probably a couple series too many.