All sorted, but remains a bit of mystery. A quick check with a meter showed no voltage on the main input terminal of the large fuse box. Tracing the cable between the battery and this terminal caused the battery clamp to come away in my hand, showing the cable had parted about 1 inch from the clamp. The battery end shows signs of melting, but when I stripped back the cable, the strands showed a clean break.
Anyway, patched out the break and the car is fine. I can't think of a reason for this - if it did melt, then there must have been excessive current into the fuse box, but no fuses are blown...
I can only conclude that in removing the red plastic cover from the battery terminal, the car park guy must have broken an already weakened cable. Still, all's well that ends well, and a fairly simple fix.