So to start from the known this then is Mary Ann for definite on the 1901 and 1891 censuses with husband John.
1901 census RG13 378 folio 160
2 Hope Street Newington
Mary Sutcliffe 32 Rotherhithe London Wife Married
John Sutchiffe 32 Newington London Head Married General Labourer
Mary A E Sutcliffe 10 Newington London Daughter
Florence Sutcliffe 6 Newington London Daughter
John J V Sutcliffe 4 Newington London Son
Henry Sutcliffe 2 Newington London Son
1891 census RG12 360 folio 87
62 Faraday Street Newington
John Sutcliff 53 Todmorden Manchester Head Married Coal Porter
Mary E Sutcliff 51 Thaxted Essex Wife Married
Martha Sutcliff 22 Bermondsey London Daughter Packer
John Sutcliff 20 Bermondsey London Son Married
Hannah Sutcliff 18 Bermondsey London Daughter Packer
Sarah Sutcliff 15 Bermondsey london Daughter Packer
Rhoda Sutcliff 11 Bermondsey London Daughter
Mary A Sutcliff 19 Rotherhithe London Daughter in law Married
Mary A E Sutcliff 2/12 Walworth London Granddaughter
So a birth year varying between circa 1872 and 1869 but consistent with the birthplace of Rotherhithe.
This is a map showing the different parishes mentioned that form a line along the south side of the River Thames
http://www.eastsurreyfhs.org.uk/parishes/parish_map.htmThe further east you go generally speaking the poorer you get. Whether Mary Ann was actually born in Rotherhithe or not she certainly thought she was so you would probably expect that her formative years at least were spent there.
Have you looked for a baptism in St Mary Rotherhithe registers?
When illegitimate people marry it is always difficult to tell how much they fabricate about their fathers. They change the surname to match their own but the other details could be correct, or are the details of a stepfather or other close male relative.
Not all births were registered. Not all births were registered in the surname you expect. Hannah can appear in records as Anna or worse Ann.
Bermondsey and Rotherhithe by 1869 were part of the St Olave Southwark poor law union not the St Saviour union.
Christchurch workhouse - St Saviours workhouse has existing records for births 1848-94 and creed registers 1856-1938. There are also poor law removal records 1866-1930.
A creed register for instance (which is the nearest you have to an admission register for this period) not only gives the creed - the religion of the person being admitted, but also where they are admitted from and when, crucially their age or year of birth and when they were discharged. A removal order would give more information.
Regards
Valda