If you have his exact date of birth from the 1939 register, you can search England & Wales deaths on Ancestry (upto 2007 is complete, 2007-2013 is a partial index)and include the date of birth as part of the search. If there are no results, it can infer that he died before 1969 which is when dates of birth were included in the index. But not conclusive.
The 1939 register was compiled in a similar way to the census, if he wasn't with his wife (he was at work) at the time, she will be recorded elsewhere.
To complicate things, his name is quite frequently occuring in the marriage index.
If you were doing this professionally you would need to buy all marriage certs in his name between 1928 and 1939 to see if you can identify him.