Do non-Americans actually still refer to "miles" a lot?

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Inperial lengths are used in British regulations of:

the mile, yard, foot and inch for road traffic signs, distance and speed measurement.
the imperial pint for the dispensing of draught beer and cider, and for the sale of milk in returnable containers,
the acre for land registration
the troy ounce for transaction in precious metals.

And it is generally not allowed to use (solely) imperial units in official contexts beyond that. Newspapers vary in their style guides, but if they target older, more traditional demographics they use imperial. Habitual use of metric is common, but it's very random. I for one, know my height in feet and my weight in stones, but my waist and hips in metric. I would estimate short distances with metres, but long distances with miles (just sounds more descriptive than kilometres). In my studies I always use metric (obviously) but if I was talking to my grandma I would flip to imperial. I only use Celsius for Temperature - I have a better understanding of Kelvin than Fahreinheit. And so on.

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Yes, speeds are cited in mph. The authorities often muse about changing them, and I think a lot of modern railways and tramways use metric, but it's all a big mess:

http://www.metric.org.uk/the-mess-we-are-in