Her birth registration date:

Surname   First name(s)      District   Vol  Page
Births Sep 1863   (>99%)
LIVERMORE Ellen Mary Newmarket 3b 505
________________

In the 1881 census she was with her father and his new wife, Emily, in the Water Mill, Fordham, Nr Newmarket.

In the 1891 census she was with her sister Martha and her husband, Sidney Webb, in Mill Lane, Soham.
________________

The following marriages are possibilities, particularly the first:

Surname First name(s) District Vol  Page
Marriages Sep 1895   (>99%)
Livermore Ellen Mary Hackney 1b 1020
Marriages Jun 1911   (>99%)
Livermore Ellen M Maldon 4a 1297   
Surname First name(s) Spouse District Vol  Page
Marriages Sep 1919   (>99%)
Livermore Ellen M Hughes Edmonton 3a 1288

The first marriage was to either Albert Edward Cooper or David Frankland.

In the 1901 census there was this entry, where I suspect she was more correctly ‘daughter-in-law’ and indeed that is what was on the enumerator’s form (told ‘em):

Surname  Forename  Age  Relation  Occupation  Birth Place

Cooper Susan 77 Head Inn Keeper Ely, Norfolk
Cooper Albert 37 Son Plumber Fordham, Cambridgeshire
Cooper Ellen 37 Sister In Law Snailwell, Cambridgeshire
Cooper Victor 5 Grand Son Fordham, Cambridgeshire
Cooper Hannah 3 Grand Daughter Fordham, Cambridgeshire
Cooper Winipeda 11 MO Grand Daughter Fordham, Cambridgeshire

Ref: RG13/1542/~F147

Address: River Lane
Parish: Fordham
Registration District: Newmarket
________________

And in 1911 there was another son, Robert Charles, Hannah had changed her name, apparently, to Agnes Laurina, Winifreda/Winipeda was now Winfreda and Ellen stated that she had had five children of which one had died:

Surname Forenam  Age  Gender  Relation  Marriage Status  Years Married  Occupation  Birth Place

Cooper Albert Edward 47 Male Head Married 15 Publican & Plumber Etc Fordham, Cambridgeshire        
Cooper Ellen Mary 47 Female Wife Married 15  Snailwell, Cambridgeshire        
Cooper Victor Ernest 15 Male Son Single - Plumber Etc  Fordham, Cambridgeshire        
Cooper Agnes Laurina 12 Female Daughter -  - School   Fordham, Cambridgeshire        
Cooper Winfreda 11 Female Daughter - - School  Fordham, Cambridgeshire        
Cooper Robert Charles 9 Male Son - - Fordham, Cambridgeshire

Reference: RG14 - PN9196 RD183 SD4 ED2 SN142

Address: Fox Inn, River Lane, Fordham Nr Soham, Cambs
Registration District: Newmarket
Sub District: Soham
Civil Parish: Fordham
__________________

My guess is that her fifth child was born after Robert Charles, but there are too many Cooper births in the newmarket district to identify that child.
__________________

This might be her death, the only Ellen M Cooper in Cambridgeshire from 1910 to 1960.  But there were other outside the county:

Surname First name(s) Age District Vol  Page
Deaths Jun 1950   (>99%)
COOPER Ellen M 86 Cambridge 4a 263
__________________

This is her most likely marriage, probably in London because she was already pregnant with Victor:

Surname First name(s) District Vol  Page
Marriages Sep 1895   (>99%)
Cooper Albert Edward Hackney 1b 1020
Livermore Ellen Mary Hackney 1b 1020
_________________