This might be Mary's birth on Familysearch
Name Mary Teresa Hughes
Gender Female
Birth Date 06 Sep 1880
Birthplace Dublin, Dublin, Ireland
Father's Name Michael Hughes
Father's Birthplace Of 23 Hammond Lane
Mother's Name Anne Keating Hughes
Mother's Birthplace Of 23 Hammond Lane

Is this your Mary Walker nee Hughes

UK and Ireland, Find A Grave Index, 1300s-Current
Name: Mrs Mary Cristina Walker
Birth Date: 4 Apr 1883
Birth Place: Dublin, County Dublin, Ireland
Death Date: 1 Nov 1945
Death Place: Nottinghamshire, England
Cemetery: Retford Cemetery
Burial or Cremation Place: Retford, Bassetlaw District, Nottinghamshire, England
Has Bio?: Y
URL: http://www.findagrave.com/cgi-...

Details from site

Birth: Apr. 4, 1883
Dublin
County Dublin, Ireland
Death: Nov. 1, 1945
Nottinghamshire, England

born Dublin always called herself Mary Cristina Pilomina Hughes married Islington ,lONDON 1908 to James Henry WALKER

Burial:
Retford Cemetery
Retford
Bassetlaw District
Nottinghamshire, England

Created by: elizabeth park
Record added: Jul 24, 2013
Find A Grave Memorial# 114310413

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1911 England Census
Name: Mary Walker
Age in 1911: 27
Estimated birth year: abt 1884
Relation to Head: Wife
Gender: Female
Birth Place: Dublin, Dublin, Ireland
Civil Parish: Islington
County/Island: London
Country: England
Street address: 1 Carville Street, Durham Road, Finsbury Park N
Marital Status: Married
Years Married: 3
Estimated Marriage Year: 1908
Registration district: Islington
Household Members:
Name Age
James Henry Walker 31, b Leeds, York, Horse keeper
Mary Walker 27
Adelaide May Walker 1, b East Finchley (age 1 year & (2)? months, hard to read the number of monthe)

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If Burial record above information in correct this could be possible birth registration.

Ireland, Civil Registration Births Index, 1864-1958
Name: Mary Christina Hughes
Date of Registration: Apr-May-Jun 1883
Registration district: Dublin South
Volume: 2
Page: 679
FHL Film Number: 101059

There are a couple of trees on ancestry who have Mary, James Henry Walker and their children and have her parents listed as

Martin Michael Hughes 1843 Knock More Ireland - 1892 Dublin

Catherine Allen 1850 Ireland - Unknown

married 1870 Dublin Ireland.

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1881 England Census

Name: Mary Hughes
Age: 2
Estimated birth year: abt 1879
Relationship to Head: Daughter
Father: Michael Hughes
Gender: Female
Where born: Normanton, Yorkshire, England
Civil Parish: Normanton
County/Island: Yorkshire
Country: England
Street address: Castleford Rd Dunnils Buildings
Household Members:
Name Age
Michael Hughes 38, head, widow, Bricklayer, b Knockmore Ireland
Edward Hughes 8,son, b Hadley Hall York
Ellen Hughes 7, daug, b Kippax York
John Hughes 4, son, b Normanton York
Mary Hughes 2, daug, b Normanton York
Kate Lyons 18, sister in law, Dom Housekeeper, b Hadley York

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Catherine Allen is listed as Marys mother

Mary Lyons is listed as John's mother

Unknown mother for Edward & Ellen

The information doesn't quite fit together,but may be worth checking.

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There is another 1881 Census for Michael Hughes with daughter Mary 1873, both born Ireland

1881 England Census

Name: Mary Hughes
Age: 8
Estimated birth year: abt 1873
Relationship to Head: Daughter
Father: Michael Hughes
Mother: Mary Hughes
Gender: Female
Where born: Ireland
Civil Parish: Parr
County/Island: Lancashire
Country: England
Street address: 21 Rimmer St
Household Members:
Name Age
Michael Hughes 30, head, Ireland, Chemical Laborer
Mary Hughes 30, wife, Ireland
Mary Hughes 8, daug, Ireland***
John Hughes 4, son, Ireland
Thomas Hughes 3, son, St Helens Lancashire
Kate Hughes 1, daug, St Helens Lancashire

There are quite a few other families from Ireland in the street with Head of house also Chemical Laborers.

WOW

1/The birth of Mary Teresa Hughes ,I am almost certain that we can discount(but will store the info)
2/The findagrave Mary Walker -IS-my grandma but the details were added by a cousin a few years ago(with nothing to justify some of the details mentioned)
3/ 1911 census -IS -also my grandparents(we know that they moved to East Retford in 1915 (James had a long career in the Essex reg (have his details and that of his family etc)-but have nothing on Mary before her marriage-
3/the birth reg for Mary Cristina-we have received a copy of this birth cert but states that father was Matthew Hughes(not correct has on marriage cert name of father is Michael Hughes a laborer
4/1881 census-I did a lot of work on this family birth, death, occupation records and was finally able to discount this family when I was contacted by a Lyons family tree owner to which I past on the research
5/the census for Lancashire-I must have missed this entry and will be looking at this one
6/I have seen the trees on various websites but I have also managed to deduce that the info does not seem correct
so once again -wow and thank you for bothering to look

Normally I would advise to get the birth for Thomas or Kate, but there are quite a few options.

I think the nearest Reg office would be Prescott, so it might be worth a search for Thomas around 1877-1878

Births Mar 1877
Hughes Thomas Prescott 8b 690

Births Dec 1877
HUGHES Thomas Prescott 8b 686

Births Mar 1878
Hughes Thomas Prescott 8b 648

Births Sep 1878
HUGHES Thomas John Prescott 8b 641

it could be any one or none of the above, but might be worth a try.

Kate may be Catherine

thank you