How do I test a class I appliance if it does not have any accessible metal earthed parts to make a connection with my lead?

If earthed metal parts are not accessible they cannot be continuity tested. Make a note on the test record that the appliance is Class I but has no accessible earthed metal parts and as such an earth continuity test cannot be performed.

Another way to view this is that the reason accessible metal parts are earthed is to provide protection against electric shock in the event of a failure in the basic insulation. If the part in question is not accessible, then there is no risk of electric shock.