Her birth:

Surname   First name(s)   Mother   District  Vol  Page

Births Mar 1921   (>99%)
O'Connor Ellen M Beaumont Holborn 1b 1074
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There are 15 Ellen M O’Connor marriages from 1938 to 1960, too many to choose from, though two of them were in Finsbury.

Brenda Graham found from her nephew Lawrence Law that Ellen May married John Byrne:

Surname   First name(s)   Spouse   District  Vol  Page
Marriages Sep 1947   (>99%)
O'Connor Ellen M Byrne Finsbury 5c 1497
Byrne John A O'Connor Finsbury 5c 1497

FreeBMD shows these Byrne children with O’Connor mothers from 1947 to 1960; I have no idea which were theirs but might guess that the Paddington one have a chance:

Surname   First name(s)   Mother   District  Vol  Page

Births Sep 1947   (>99%)
Byrne Cornelius T O'Connor Hendon 5f 396
Births Dec 1948   (>99%)
Byrne John O'Connor Islington 5c 1594
Births Jun 1951   (>99%)
BYRNE Richard J O'CONNOR Hendon 5e 625
Births Sep 1951   (>99%)
BYRNE Vincent J O'CONNOR Paddington 5d 236
Births Mar 1952   (>99%)
Byrne Mary T O'Connor Birmingham 9c 344
Births Sep 1952   (>99%)
BYRNE Mary C O'CONNOR Paddington 5d 258
Births Sep 1954   (>99%)
Byrne Helen E O'Connor Paddington 5d 267
Births Dec 1954   (>99%)
Byrne Edward A O'Connor Nthmbld.W. 1b 558
Births Mar 1956   (>99%)
Byrne Francis O'Connor Chester 10a  273
Byrne John M O'Connor Nthmbld.W. 1b 639
Births Dec 1956   (>99%)
Byrne Agnes A O'Connor Hammersmith 5c  687
Births Mar 1957   (>99%)
BYRNE Angela O'CONNOR Willesden 5f 328
BYRNE Christopher J O'CONNOR Liverpool S.   10d  753
Births Sep 1957   (>99%)
BYRNE Doris A O'CONNOR Kensington 5c 1531
Births Mar 1958   (>99%)
BYRNE John J O'CONNOR Ealing 5e 212
Births Mar 1959   (>99%)
BYRNE Thomas P O'CONNOR Prescot 10f  389
Births Dec 1959   (19%)
BYRNE Colin D O'CONNOR Ely 4a 509
Births Jun 1960   (13%)
BYRNE Paul M O'CONNOR Kensington 5c 1735
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