We were somewhere around Barstow, on the edge of the desert, when the
drugs began to take hold. I remember David Robinson
saying something like:

Thirdly, the supplied cable has a standard IEC_60320 C7/C8 at one end,
but a UK mains plug without a fuse at the other end. The mains plug is
very small and almost clover leaf shaped - barely 5mm larger than the
pins in any direction.

Yep, I bought a HK-made *but UK-supplied* light box a couple of years
ago with the identical plug on it.

Is it legal to have a UK plug without a fuse when it feeds a flex? The
plug is marked 250V 10A.

Quite illegal, afaik, and bloody dangerous, imo.