Many thanks for all the very kind comments, folks - you spoil me.
A couple of nights ago I finally decided to investigate why 'Kaffie' had stopped running late on the Saturday afternoon at Pewsey. I dropped the mech out of the body - easy to do, as I had had the unexpected foresight to secure it with the couplings, which just have to be pulled out.
Then I applied power to the wheels - deathly silence. I removed the motor - just one screw on the underside - and applied power to the terminals - a nice busy whirring noise. Obviously a problem with the contacts to the motor inside the chassis - Hornby have put a strip of brass on each side that has contacts to the back of the wheels and to the motor when it's in place, rather than wiring it in. So, fiddle with the motor part of the strip, replace motor, apply power to the rear wheels - wheels spin round. Apply power to front wheels - deathly silence. Obviously one of the wheel parts of the contact strips isn't in contact. Remove motor, fiddle with contact, replace motor, apply power the rear wheel - deathly silence.
Over the next hour or so I went through the cycle of motor out, fiddle with contacts, replace motor, apply power many times. There were three different results:
1. Deathly silence.
2. Power to rear wheels, wheels spin, power to front wheels, deathly silence.
3. Power to rear wheels - buzzing sound from the mech but wheels stay still.
The contact strips became more and more distorted as I tried different bends and angles to get good contact to motor and both sets of wheels. Result 3 became more and more common, even with power to front wheels, so I finally allowed that there was something fundamentally wrong in the state of Denmark. I removed the motor once again and looked closely at the inside of the chassis, and noticed ...

... the buzzing sound had been the worm gradually destroying the gear on the front axle - I had been wondering what the white powder on the inside of the chassis was - ground-up gear.
After a period of contemplation I think I know what was basically amiss. The chassis was second hand and in rather less then as-new condition, so I replaced the old-style motor with a new motor and mount, but the large side flanges that locate the motor and hold the wire retaining spring -

- fouled the new motor, so I cut them off and glued the motor to the mount. Sadly, I didn't quite get it straight, so the worm was a little right of centre. At the same time, the front wheels are a little over gauge, and the contacts pushed them to the left, so the mesh was a bit dodgy, to say the least. It was good enough to run the loco at first, but my frenzied efforts to sort out the contacts had worsened the problem, and repeated applications of power produced the resulting ruined gear - the worm is unharmed ...
As Hornby don't allow their wheel sets to be dropped out for replacement the chassis is now effectively a non-runner. Fortunately, I have laid in several spares chassis, so I shall remove all the usable bits from the old one and use the remains as the pattern for a new one - taking great care to get the gears to mesh properly ...
Hours of fun ...