I noticed a tingling from contact with a USB lead of an external Hard Drive.

Investigating this led to the PSU, the plug of which has a high voltage
on the outer connector compared with house earth. It was varying between
70 and 110V.

(I did not check the voltage of the output which I have no reason to
doubt was correct - 12V I think it should be)

The PSU is a three pin plug. Presumably the earth connection is not
being used.

Is the PSU faulty?