Thanks for the reply Ian,
I left my meter powered up all day. Since I saw yours do the same as mine, I've decided it isn't faulty.
I've removed the front panel and given everything a good clean and polish.
The wires to the 4mm sockets just pull off, but the white wire on the Amps jack doesn't.
You need to remove the fuse and then the spring and contact can be unthreaded through the bottom of the fuseholder moulding.
After it's been in bits, cleaned and made to do some work, it seems to behave a lot better.
The mV offset is showing 0.0015mV at the moment, but it was 0.0089mV just a few minutes ago.
Given the input impedance of the unit, I think there may still be some absorbed moisture that needs to be driven out.
Simon.