There are too many other Robert M Wilsons to identify his birth or death, even though we know his exact birth date.

With his birth date from the 1939 census of 23 Nov 1885 and his second forename of Macgregor from his wife’s probate, this has to be his birth index:

First name(s)         Robert Macgregor
Last name             Wilson
Birth quarter         1
Birth year            1886
Mother's maiden name  -
District              West Ham
County                Essex
Country               England
Volume                4A
Page                  249
Record set            England & Wales Births 1837-2006

This then led to these two birth indexes on the new GRO site including his mother’s maiden surname:

Name:                Mother's Maiden Surname:
WILSON, ROBERT       RYDER  
GRO Reference: 1886  M Quarter in WEST HAM  Volume 04A  Page 59
WILSON, ROBERT       SWARBRICK  
GRO Reference: 1886  M Quarter in WEST HAM  Volume 04A  Page 248

Note that the page number is 248 in the original index and 249 in the new version, so my guess is that his mother was Swarbrick.

So I need to have a look at the odd census to (try to) sort this out.
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His likely baptism which ties up with the following census:

First name(s)           Robert Macgregor
Last name               Wilson
Baptism year            1886
Baptism date            27 Jan 1886
Father's first name(s)  John
Father's last name      Wilson
Father's occupation     Civil Engineer
Mother's first name(s)  Emily Jane
Place                   Woodford Wells
Residence               Fern Bank Mornington Road
County                  Essex
Country                 England
Archive                  Essex Record Office
Archive ref             D/P 508/1/1
Record set              Essex Baptisms
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This 1891 census looks a good match at The Firs, Woodford Road, Wanstead, West Ham, London:

First name(s)  Last name  Relationship  Marital status  Sex  Age  Birth year  Occupation  Birth place
John        Wilson   Head      Married  Male    45  1846  Civil Engineer  Scotland
Emily I     Wilson   Wife      Married  Female  43  1848  -               Manchester
Edward A    Wilson   Son       Single   Male    15  1876  Scholar         Cheltenham
Florence M  Wilson   Daughter  Single   Female  13  1878  Scholar         Cheltenham
Herbert S   Wilson   Son       Single   Male    12  1879  Scholar         Tottenham
Margaret    Wilson   Daughter  Single   Female  10  1881  Scholar         Tottenham
Ellinor     Wilson   Daughter  Single   Female   8  1883  Scholar         Tottenham
Robert M G  Wilson   Son       Single   Male     5  1886  Scholar         Woodford, Essex
Francis     Nash     Servant   Single   Female  33  1858  Domestic        Rotherhithe
Agnes       Beckett  Servant   Single   Female  20  1871  Domestic        Chelmsford, Essex
Eliza       Cook     Servant   Single   Female  20  1871  -               Stratford
Henry       Homard   Servant   Married  Male    30  1861  Gardener        Walthamstow
Emily       Homard   Servant   Married  Female  30  1861  -               -
Henry P     Homard   Boarder   -        Male     5  1886  -               Chingford, Essex
Emily E     Homard   Boarder   -        Female   3  1888  -               Wanstead, Essex
Lilly E M   Homard   Boarder   -        Female   0  1891  -               Wanstead, Essex

Ref:
Archive reference  RG12
Piece number       1352
Folio              67
Page               36
Combined:          RG12, piece 1352, folio 67, p. 36
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On the 1891 census their oldest child was then 15, so it is likely that they married before his birth in 1876.  And in fact they did marry in Q3 of 1873, in Edmonton, Middlesex.

So far everything hangs together that Robert Macgregor Wilson was born on 23 Nov 1885 in Fern Bank Mornington Road.  But this does need a little more confirmation and would need Robert’s birth certificate.  But I am only going to buy that if I can find that Robert and Ursula had a child that survived.
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His probable probate index, very likely for him if his mother was indeed Emily Swarbrick so that his executor was a relation of hers:

1950
WILSON Robert Macgregor of East Sussex Hospital Hellingly Sussex died 27 February 1946  Probate London 17 February to Edgar Swarbrick solicitor.
Effects £3269 18s. 4d.  By decree dated 27 January 1950.

His will has been ordered in case he had a child mentioned within it.  The wrong will seems to have been ordered and delivered!
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Note that another Robert Macgregor Wilson died in 1976, leaving a will and a few more pennies.  But he was born in 1913.
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The probate document includes that the Hospital of his death was a ‘Mental’ hospital and this raises questions of the validity of his will which were taken to the High Court and on the 27th Jan 1950 pronounced valid.  His net estate was £2936 and all of this was left to his sister Elinor Winzor.  His will was dated 22 April 1943.

So, no children found.
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Their marriage index:

First name(s)       Ursula M J
Last name           Carroll
Marriage quarter    3
Marriage year       1938
MarriageFinder      Ursula M J Carroll married one of these people
                    Robert M Wilson
Spouse's last name  Wilson
District            Kensington
County              London
Country             England
Volume              1A
Page number         668
Record set          England & Wales Marriages 1837-2005
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