There are two Greenans born in Yorkshire with the sole forename of John between 1900 and 1940, one in 1904, which is really a tad old and one in 1918, which is credible.  Let’s see what comes of that:

His possible birth index:

First name(s) JOHN
Last name GREENAN
Birth year 1918
Birth quarter 3
Mother's maiden name Revie
District Middlesbrough
County Yorkshire
Country England
Volume 9D
Page 894
Record set England & Wales Births 1837-2006

There are no births in Durham.
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This is the only death of this John Greenan, born from 1916 to 1920, in Yorks and Co Durham, with birth date:

First name(s) JOHN
Last name GREENAN
Gender Male
Birth day 11
Birth month 9
Birth year 1918
Death quarter 1
Death year 1994
District Central Cleveland
District number 3481C
Register number C43
Entry number 248
Date of registration mm/yy 0194
County Yorkshire
Country England
Record set England & Wales Deaths 1837-2007

He could, of course, have died after 2005 when the internet death records cease.
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And the same John Greenan, with his parents, appears in the 1939 Register:

38 Drake Street , Billingham U.D., Durham, England

FIRST NAME(S) LAST NAME(S) DOB SEX OCCUPATION MARITAL STATUS  SCHEDULE  SCHEDULE SUB NUMBER

John Greenan 11 Sep 1918 Male Platelayer Labourer Heavy Worker  Single  303  4
Hugh Greenham 11 Aug 1888 Male Metal Calciner Heavy Worker  Married  303  1
Grace Greenham 29 Apr 1895 Female Unpaid Domestic Duties  Married  303  2
Elizabeth Wright (Greenan) 11 Dec 1916 Female School Caretaker's Helper  Single  303  3
Sorry, this record is officially closed. Check if you can open a closed record.
Sorry, this record is officially closed. Check if you can open a closed record.
Sorry, this record is officially closed. Check if you can open a closed record.

Ref: RG101/2743J/004/5

The Greenham surname for his parents is a transcription error, I have told ‘em.
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Their marriage index:

First name(s) ANNE
Last name MELLON
Marriage quarter 3
Marriage year 1957
ANNE MELLON married one of these people:
John Greenan
Spouse's last name Greenan
District Durham South Eastern
County Durham
Country England
Volume 1A
Page number 1752
Record set England & Wales Marriages 1837-2005
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