Update for anyone who's interested.
BMW dealer apologised and immediately posted a 13 pin Continental to 7 pin UK adapter.
Job done - trailer socket works! All I've got to do now is put the Thule on!
318i E36, 320i E36 Touring, 530DSE E39, 525DSE E60,
325i Sport E46, 318Ci Convertible E46, Now in an X1 sDrive20d SE E84