Free BMD brings up two Patrick Williams's married to Jo's in the early '60s, none in the mid/late '50s.
One, Patrick J. Williams, married Joyce Holland in Bolton, 1st qtr 1961.
The other, also Patrick J, married Joan Green in Swindon, 3rd qtr '63
If these look likely you may be able to further information from local newspapers of the time.
Although the collar dogs do look a bit like the Devons' star and crown the centre of the badge seems to be of a dark colour, possibly even enamelled. From memory I don't recall the castle in the Devon's dress badge ever being anything other than silver.
Looking at a blowup of your photo I wonder if the central device is a rose ? I can't find a badge like this but wonder if it is one of the Lancashire Regiments ?
Maec