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I have that in stock in the UK

Typical.

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I have a feeling that UK and US back boxes are incompatible

As Trevor said, yeah, they are. In the US, they are 3" tall by 2" wide (internal) by about 2.5" deep (though that varies), although we call them "junction boxes", "outlet boxes", "switch boxes" (while outlets and switches are almost always on separate plates, the boxes in the walls are identical), or simply "electrical boxes". They also make them that are basically multiple ones joined together usually without what would become internal barriers, for when you need multiple switches at one wall location.

I should just install one of those double-gang boxes and a whole new switch, but I don't want to have to rip apart the wall. I could potentially abut a new single-gang "old work" box (where the box holds onto the wallboard instead of being nailed onto a stud), but the chances of me aligning it right are slim.
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Bitt Faulk