On my car I did not fit an electric socket only the tow bar and tow ball. And it PASSED (2012/2013/2014) 3 MOTs at 3 different garages without any comment.
If NO electric socket is fitted it cannot be tested. Also see....
UK MOT Information, Electrical Wiring and Battery
Note 3.
On vehicles fitted with a towbar, check the condition and security of the trailer electrical socket.
Note: This check applies to both 7 pin (12N) and 13 pin electrical sockets.
Note 4.
On vehicles fitted with a
trailer 13 pin Euro-socket, use an approved device to check that the socket is wired to correctly operate the trailer:
. Position lamps
. Stop lamps
. Direction indicators
. Rear fog lamp
And....If
a tow ball or pin is not fitted at the time of test, e.g. because it is
detachable, has been
unbolted or otherwise removed, but the attachment brackets are still in place,
any (that's present) trailer electrical socket/sockets should still be assessed.