It is a weird mix in the UK, distances are measured in miles, and speed limits are set in miles per hour, but fuel is sold in litres, for example.
People get very worked up about it too. People got very worked up about a government proposal to allow people to put imperial units on food in larger type than metric (at the moment it has to be metric larger - or at least the same size).
Everything in engineering and science has been entirely metric since the 80s.
Only road distances for cars are in miles and yards. The British railways continue to use chains (which are not used for any other ordinary activity) and non-road traffic is often in metres or kilometres as appropriate.
Some of those "Metric martyr" types, the kind of people who think anything which changed after they were 35 is an abomination, but somehow anything which changed ten years before they were born has never been any other way, will vandalize legal stuff which uses (in their opinion) the wrong units. So if you put a (legal and reasonable) 1.5km distance sign on a cycle route, but some car driver who thinks sane units are fascism sees it, they might smash it to pieces which is annoying.
There has been a very gradual lean towards sanity, after all my mother was taught decimal currency because it was forthcoming when she was at school, her parents had used a non-decimal currency system. When I was a teenager I still had coins which, though they were treated as their modern decimal value, if you read their faces had a non-decimal value printed on them, because it's too expensive to replace the currency when you switch.
When I was a child I would buy a quarter pound of sweets. At the turn of the century I'd ask for, and receive, 100 grams or 200 grams as I felt, but most customers would use pounds (although legally they'd be served in grams). These days everybody else would likely also ask in grams. So it's changing, it's just very slow.
The whole yard vs feet thing is especially weird. Indeed, in US as well, feet are normally used to measure sizes - at scales where it's reasonable - while yards are normally used to measure distances. Even though the two units are in the same ballpark / order of magnitude. And yes, as you rightly point out, it means that few people can estimate distances in feet.
OTOH on road sings, US at least seems to be using miles alone consistently, so you end up with labels like "1 3/4 miles" every now and then, which I find to be difficult to parse quickly.
Distances in the UK are measured in miles and yards (or fractions of a mile). Google Maps gets this wrong and uses miles and feet. I don't think many people in the UK have a good intuition for how far 500ft is.