Sound ta Sparks. Hopkirk I would not even plug it in after what you have told us. The fact that it is a drier to boot doubly so. Not really a job for a D.I.Yer I am afraid. I would be changing the mains lead then before plugging in then getting out my trusty Avo meter to do leakage tests.
You say it triggers the RCD when you plug in the drier so that must be the cause. Whether the w/m has an problem too is a separate issue, but you don't seem to have posted any evidence for that.
Oops ....... I wondered if you meant the RCD. They will operate on a neutral fault as well as a live fault.
Check the plugs first, then have the appliances tested, Hops.
Hoppy....you may find that damp has got to vulnerable electrics within the dryer..you could investigate..or just get your wallet out..p.s.ditch the test screwdriver..(Togo's pet hate)