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I am sure that Grace born 1850 is Kate's older sister. Grace is on 1851 census as 10 months old so that fits, and Charles is 5, so would be approx 10 when Kate born. That would make details of the 1891 census correct when Charles is lodging with Kate and Elias Park.
Can anyone help me find out if the family were possiblyHuguenot as there are a lot of Desmoulins christened between 1722 and 1738 at a French Huguenot church in Threadneedle Street, all with the same parents, Jean Desmoulins and Judith(Judig) Huet.

Just posting these in case they have any connections

Births Jun 1850
Dumoulin Grace St. Lukes 2 319

Births Sep 1854
Deneulain Mary Ann Stepney 1c 498

Births Mar 1856
DENEULAIN Ellen Louisa Stepney 1c 490

Yes I have checked out a lot of Demoulins in Belgium and France - how much time can you waste tracking the wrong people!! I am really going on my Mum's memory of her being French but until I find the parents it's a puzzle.I traced a John and Jane Dumoulin on the 1851 census with children including Charles and Grace - knowing how popular it was to call children after relatives it may explain why Kate called her daughter Grace (my grandmother). John Demoulin was born about 1812 and I have found a marriage between John Cornelius Du Moulin to Grace Davidson in 1811, and Jas (Joseph?) Adrianus Dumoulin to Jane Davidson in 1812, both in Limehouse. Both names suggest Dutch Belgium or French descent?
Can anyone suggest how to find out more - I have searched all the census and can't trace much more so again the name may have changed to become more anglicised.
A bit of family history - soon after Kate died her daughter Grace went with my mum to a spiritualist evening. She was told that there was an old lady standing in the corner shaking...Kate died of Parkinson's disease, which no-one there knew. Grace was very upset, and my mum has never forgotten it. If only Kate would send me a message now!!

the name does appear to come mostly from Belgium - example

Husband
Théodore Joseph Demoulin Pedigree


Birth:
Christening:
Marriage:
Death:
Burial:





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Wife
Anne Josèphe Chenet Pedigree


Birth:
Christening:
Marriage:
Death:
Burial:





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Children

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1. Catherine Josèphe Demoulin Pedigree
Female

Birth: 18 OCT 1759 Saint Michel, , Namur, Belgium
Christening: 19 OCT 1759 Namur, Namur, Belgium
Death:
Burial:

Thanks for the info on the surnames. My mum, who is nearly 90 and remembers Kate as Granny Park and very old, always thought that she was French. The Park family I have traced back to Holland with the help of other GR members, and I just had a feeling that the families may have come from the same area. On the 1891 census Kate & Elias were living with their children and a Jane Dumoulin who I think may have been her mother, and possibly brother Charles who is also on the 1901 census.
I have ordered the marriage certificate so hopefully I can find out more.
Thanks again for your help
Claire

for interest.....

Demoulin Name Meaning and History
French: topographic name, with the preposition de, from moulin ‘mill’, or a habitational name from any of the numerous places named with this word. See also Moulin. In French-speaking countries Dumoulin, or the plural, Desmoulins, is the more common form. All are frequently translated as Miller.

Dumoulin Name Meaning and History
French: from du moulin ‘from the mill’, applied as a topographic name for someone who lived at a mill, or, by extension, as an occupational name for a miller. In North America this name is particularly associated with Fonteneau (see Fontenot). See also Demoulin.

Distribution of Dumoulin Families in England and Wales in 1891...
Minor in Lancashire and Surrey
Majority in London

Do you have Elias & Kate's marriage certificate ?
It should give you their fathers names

England & Wales, FreeBMD Marriage Index: 1837-1983 about Elias Park
Name: Elias Park
Year of Registration: 1875
Quarter of Registration: Oct-Nov-Dec
District: Mile End Old Town
County: London, Middlesex
Volume: 1c
Page: 1257

Can anyone help me trace Kate? She was born about 1856 in London and married Elias Park 1875, registered at Mile End Old Town. She died in 1935 I think. Her daughter Grace born 1890 was my grandmother, who died 1938. The surname may have been Dumoulin originally, and I think the family came from Holland, as did the Park family.
Thanks a lot - Claire