Thanks everyone: for information, I tried everything suggested except the bag and pulling out the plug. But JM's suggestion put me on the right track.
What was happening (somehow, although LAN restart was disabled) was that the router was sending out a 'where are you?' signal 12 s after shutdown, and the computer was unable to resist...
I enhibited the restart by disabling the "Restart by PCI PME" function in the MoBo setup pages. Shouldn't have any effect, but it does.
Thanks for all the fun, chaps.
Jim