Update:

Well, this is proving an odd one!

I have had no more RCD trips whilst the washing machine is unplugged, so maybe just coincidence before that the cct tripped without it plugged in.

I took the advice to remove the motor and blow out any carbon dust. Actually, there wasn't really any dust there and all looked in good order with the brushes. I plugged the WM back in, with the motor disconnected and there was no RCD trip.

I then tried it with the newly cleaned motor reconnected and still no trip RCD. Hooray! Except that was a little premature.

I ran the machine with the back off and all tickety-boo. But when I pushed it back under the worktop and put some washing in, it ran for only a few minutes before tripping the RCD. Drats!

So this time, a full test with a different cct/RCD and still it trips the RCD, so I think that rules out the RCD.

I've dismantled the whole front and got the control panel off. Checked the PCB over and no sign of burning or anything like that.

When it's all connected, I got these strange resistance readings:-

Switched off gives:-
E-N = 500KOhms (all approx)
E-L = 700 KOhms

Switched on gives:-
E-L = 800 KOhms
E-N = 980 KOhms

Switch back off gives (strange this):-
E-L = 1.5 MOhms
E-N = 1.5 MOhms

Testing across the mains filter that is at the back of the machine, immediately connected to the incoming cable, gives:-
E-L = 330 M Ohms
E-N = short (0-ish Ohms)

If I disconnect the front control panel then plugging in the WM doesn't trip the RCD. But if I reconnect everything back up, then it trips immediately.

I'm afraid I don't know enough about those filter things, but is that E-N short correct? Could it be the filter that's duff?

The control panel has a big sealed switch for the main control know, so I've no idea what the contacts are like inside. Moreover, I don't know if it's possible to buy another panel (economically at least) or if it's just time for a new washing machine.

Thanks again gents for all your expertise. Hoping someone might know a next step to try.