Thanks to all for the suggestions. A few comments:-
Probing along a track sounds like a good idea, but the reality is that the surface tracks are 6 thou wide, covered with solder mask, and very easy to destroy. There are no surface power tracks, apart from the short connections to decoupling caps. The only practical access points are at vias and component pins. In my case, the current wasn't flowing along a surface track anyway !
Probing with a 4 wire ohmeter is doubly difficult, because you need two connections at each point. In practise this means soldering a contact in place. I got some very strange readings until I remembered about thermally generated emf's and allowed everything to cool after soldering.
So I did some simple voltage and resistance gradient 'maps', which didn't really show anything. Big puzzle - back to square zero.
Finally I realised that the reason that there was no voltage/current gradient across the board was that the measurement reference point (main Vcc decoupling cap) and short were in pretty much the same place. A few minutes later a near invisible solder splash turned up on a regulator chip which was ~ 5mm away from my reference point !
Normally I do some tests as I incrementally assemble a new board, but as this was a variant of a working design, I got somewhat careless. I'm not sure that it would have helped anyway, because the solder splash must have occurred quite a long time after the regulator was installed and tested ...
Looking back on it, I wasted hours on something that should have taken minutes, but I hope to have learnt enough to shorten the next one ...
Thanks again ! Dave