Cordless Crazy formulated the question :
What would cause the metal casing of both a microwave and a kettle to
become 'live' to some degree when plugged in to a certain socket?

The voltage is not high enough to be uncomfortable, but you certainly
can feel it. Tis a bit like a weak electric fence when touched.

However, the appliances do not do it when plugged in to another socket.

Two possibilities:-

1. The socket lacks an earth and what you feel is the normal leakage
from the appliance to earth.

2. The socket and appliances are properly earthed and you are 'live'.
In other words you are standing on or touching something else which is
at least to some extent 'live'.

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Regards,
Harry (M1BYT) (L)
http://www.ukradioamateur.co.uk