Option 1: Call a pro.
The safest and easiest approach. If you don't have the skills and/or equipment for the other options, just have the machine diagnosed and repaired by someone who does.
Option 2: Use an isolation transformer.
Just pull out your trusty isolation transformer and use it to power the machine. I'm sure you have got one, or you would have stopped at Option 1.
This ensures that both the live and the neutral conductors of the washing machine are isolated from ground and the mains, so you can't get nailed no matter which part of the machine you touch. You can also monitor the current through the equipment grounding conductor and while you wiggle or disconnect various parts of circuitry to pinpoint the ground fault.
Not really option 3: Play the Russian roulette and get yourself killed to save a hundred £/€.
This is very much against the applicable code/regulations unless you're a licensed electrician. If you're one, go to Option 2 instead. If you aren't one, go to Option 1.
You're still here? OK, whatever, it's your life (and those of your family members) anyway. Don't come back complaining when your house burns down or someone gets killed.
Disconnect the ground wire AND bond the chassis to the neutral wire instead. Triple-check that you haven't accidentally swapped live and neutral. Do not leave the chassis unbonded under any circumstances, as the ground fault would make it live and get yourself killed even sooner than otherwise expected.
If you want, you can make yourself a convenient un-grounding gizmo for this: Make a really short extension cord (so short nobody will ever want to use it for anything, like 20 cm or less) that has the ground contact(s) on the receptacle end bonded to neutral, and the ground contacts(s) on the plug end left disconnected. Clearly label this as a time-travel tool that takes you back to when dedicated equipment grounding was a rarely used luxury. Never use it to permanently workaround ground faults.
Undo these modifications as soon as you're done troubleshooting. Under no circumstances leave the machine unattended when wired like this.
Really, you should have picked one of the former two options instead.