"two-by-four" is used colloquially in the UK for stuff with that approximate cross section, but wood is generally sold with millimetre measurements.

It’s not even approximate. A typical two by four is around 1.5 by 3.5 inches, which is a full third less material than lumber which literally measures 2 by 4.

IIRC this is because "two by four" refers to the size of the rough-sawn stock, but you buy milled 2x4s, so the difference is simply what's removed in milling. You can get these odd formats (stuff like "78x34 mm") in hardware stores here, too, it's just that they're not used for construction, because construction lumber is "hard metric", i.e. nice round numbers like 40x60 mm etc.

While there's an equivalent size, those are (legally speaking) sold by the mm.

For example: https://www.builderdepot.co.uk/timber-sheets/carcassing-timb...

Note the listing is primarily in mm with the imperial measure along side.

So of course the actual size is still equivalent to the old imperial size because of the history, from a legal perspective it's metric.

Right, the size cannot easily change I suppose, for how could you repair older houses/etc? Or use older building plans?

We (Canada) partially transitioned too, but didn't complete the building supplies part of it.

So food is all metric, roads, speed limits, distances, weights, yet wood is imperial, and tools are metric and imperial.

This makes sense, because with the US so close, and the largest trading partner, imperial cannot fully vanish in some repects, until they get rid of it too.

“Two by four” is a category descriptor, not a measurement. Such products do not have dimensions which equal 2 and 4 in either imperial or metric units.

2x4 is a name of lumber that's not 2 by 4 inches at all.