As others have said, the marriage cert looks like the first step.
How sure are you about his birthplace and birth year? There are LOTS of David Thomson births for the right period in Scotlands People for instance. It really would help if you can say what you know for definite and what your source is.
Given his age, its possible that he does not appear on the 1939 register as he was likely to have been in the forces.
If you have access to Ancestry they have electoral rolls for Newcastle.
Nina and David Thomson are both listed in 1931 at 58 Mason St, Newcastle, St Lawrence Ward, along with Henry Sidney Patterson and Helen Mary Patterson
1938 and 1939 they are both listed at 78 Mason St, Newcastle
1952 David, Nina and David G (likely to be their son) at 50 Mason St
1955, 1956 David, Nina and Kenneth at 50 Mason St
1957 David and Nina at 50 Mason St
1958 50 Mason St , only has a David Thomson listed
1959 50 Mason St just has a Henry S and Marguerite E Thomson listed
There are no registers in the database for 1960-1964
and I have run out of time to firkle after that, but I'd say that your David was still alive in 1957-1958, which at least narrows down the time frame for his death and the electoral registers which list him, his wife and a son are a fair indication these are the right people.
Boo