Wow, thanks, I had no idea it would be that easy: I thought the only area filter was the bounding box.

It works great except that it takes the Sutton to mean the London Borough of Sutton, rather than Sutton the civil parish in Peterborough City Council area.

I’ve just dug up the guidance at https://wiki.openstreetmap.org/wiki/Overpass_API/Overpass_QL#By_area_.28area.29 but can’t make easy sense of it: I assume there must be a way to specify the other Sutton?