wrote

Out of the blue, my faithfull old Hoover washer tripped the RCD on my
consumer unit.

After reset, it'll stay untripped when the machine is powered on at the
socket,
but as soon as I turn the control to anything other than 'off' the RCD
trips.

The strange thing is that I've left the washing machine unplugged
and yet the RCD still tripped a couple more times,

That means the RCD itself is likely faulty, try replacing it.

In theory it could be a wiring fault to the socket you
plug the washer into, but thats not as easy to test for

but seems to have settled now and been ok for a few hours.

So, two questions:-
1. Any idea why the RCD might be tripping when machine is not plugged in

Two obvious possibilitys are a faulty RCD and
a wiring fault with the wiring to that socket.

(I'm assuming it is the machine that is faulty)

You can't assume that with those symptoms.

2. Assuming the machine is faulty,

Looks unlikely given that it does trip at time when its unplugged.

anyone know where to start looking for
what could be causing the imbalance?

Most likely a wire has come adrift or is charred etc or water has got
in where it shouldnt, but that wont be the case with your washer.

Don't want to invest in a new machine if this one could be fixed
easily/cheaply.

Note that the ring main MCB is not tripping,
just the RCD for all the downstairs breakers.

I have electrical knowledge and multimeters etc.
Just seeking opionions on what might be most likely.

Most likely the RCD is faulty but it can easily be the wiring to the socket.

Thanks, as always, for sharing your knowledge and experience.