Every single one in those search results, though, is for US plugs. There's a reason for that; in fact, there're two. In
most house walls are brick, and installing a 3.5in deep backbox would mean drilling out 3in of solid brick. But even once you'd done that, UK plugs invariable have wires that exit downwards, not outwards from the wall, so you probably wouldn't gain much anyway. If the bulk of the plug was a problem, you could install a flush-mounted FCU -- I don't know whether it's strictly pukka to have a FCU that ends in an IEC socket, but it doesn't seem like that would be unsafe in any way.
Peter