We had postcodes in Norwich before then QM - first city to have street-by-street codes in 1959 though they were of a slightly different format (e NOR 89B rather than say NR1 3ND - these are just for illustration). I think Newport (in the former county of Gwent) had an early version as well (e.g. NPT 3FN) Link at http://www.sigtel.com/tel_info_postcodes.html
I
really should get out more. ;-)
Link here: