To add a little fuel to the fire, there was a letter waiting for me from Barnardo's, saying that little Francis Thomas Jenkins had been shipped off to Canada in 1913, and was in Dashwood, in 1919, using the name Fred. No further info there. I so hope that he had a happy life....
They couldn't give me more info because I wasn't the direct descendant, but implied that the aforementioned Ellen Constance Gooch who married William Kemp in 1891 was the mother.
This then begs the question of my grandfather's father, as he was born in 1892.
Presumably Ellen left the marital home pre his birth.
The father on his birth certificate is named as John Evan Jenkins. One Jenkins .
I may never know whether I am of Jenkins or Kemp descent! 
Mmm.....
Is Ellen on two censuses in the same year?
and
Did she have John D JENKINS 28 Aug 1892 and then approx. 7 months later
have another child Jack R KEMP in Mar qtr 1893

Ellen Constance Kemp nee Gooch
age 40 is on the 1901 census with husband & child
Ellen Jenkins
age 27 is on the 1901 census with husband John Evan & 4 children
1901 RG13; Piece: 1263; Folio: 92; Page: 12
22 Hyde Square
John Evan
JENKINS 32 Hackney
Ellen 27 dittoed as born Hackney John D 8Augustus C 5
Dorothy E 2
Francis T 12 mths Edmonton
birth entryJohn David Jenkins Oct-Nov-
Dec 1892 Hackney Vol 1b P 471
1901 RG13; Piece: 1224; Folio: 123; Page: 2
9 Sheldon Road
William
KEMP 36 occ clerk
Ellen C 40 Islington LondonJack R 8 WillensdenDorothy B Robertson niece 15 Kennington London
birth entryJack Reginald Kemp Jan-Feb-
Mar 1893 Hendon Volume: 3a Page: 210
According to the
London Electoral RegisterWilliam & Ellen Constance KEMP with living at 33 West End Lane
1918/19/20/21
Ellen Constance Kemp died 31 Mar 1938
Administration 12 May 1938 to Jack R Kemp Sales manager
In 1911 I have found Dorothy Ellen as Doris Woodruff.
She was supposedly taken in by her aunt who was Annie nee Jenkins. An Annie Jenkins married Woodruff, but I haven't managed to link Annie with my John Evan Jenkins yet.
Still working on that one . ...
this looks to be Dorothy's birth entry
Dorothy Ellen Jenkins Jan-Feb-Mar 1899 Hackney Volume:1b Page: 577
did she marry?
Dorothy Ellen Street died age 78
Born 17 Feb 1899Date of Registration: Jun 1977 Hitchin Hertfordshire
Volume: 10 Page: 0507