I had a bit more of a stare at the wife's name as I could not find anything for a Edith May Adams ... Was there maybe a little"r" in May?
And with this option I dug a bit more and unearthed in the various Sth African indices:
Ethel Mary ADAMS nee CRUMPTON b 10 May 1906 , died probably between 1992 and 2008
And then following the bread crumbs to the 1939 register:
Ethel M ADAMS (CROMPTON) Single, Sorting Clerk Telegraphist, born 10 May 1906
Residence: 115 Oxford Rd, Birmingham, Warwickshire
(Of course we still don't know 100% that she is the wife of "Your' John)
Update:
https://www.familysearch.org/ark:/61903/1:1:QVD9-ZCHMEngland and Wales Marriage Registration Index, 1837-2005
Name: Ethel M Crumpton
Event Type: Marriage Registration
Event Place: Solihull, Warwickshire, England
Registration District: Solihull
County: Warwickshire
Registration Year: 1946
Registration Quarter: Apr-May-Jun
Page: 2219
Affiliate Line Number: 26
Volume: 6D
Spouse Name (available after 1911): Adams
Possible Spouse:
John S Adams(You can now order the marriage certificate and tell us whether this is "your" John)