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I presume that this is your grandmothers birth registration:

Births Jun 1916
Meux Doris L R Meux Dartford 2a 1161

If her mother visited the foster parents when her daughter was about 2 years old then presumably she was still in the UK until at least 1918.

As Penny has said there does not appear to be a birth registration of a Miriam Meux in the Thanet registration district c1894. There does not appear to be a marriage or death of a Miriam Meux in England or Wales either. I haven't got a subscription to FMP but from the free search of the passengers leaving the UK there is only one Meux showing but the birth year indicated (1868) means that unless there was a serious clerical error this could not have been Miriam.

hanging on a hunch here...

Births Jun 1893
Mew Miriam Elham 2a 1006a

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Births Jun 1895
Mew Florence Louis Elham 2a 1029

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Births Mar 1897 Mew Thomas William Elham 2a 1036

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Births Mar 1919
Mew Peter I D O Mew Elham 2a 1512

I wonder if this is her birth?

Births Jun 1893
Mew Miriam Elham 2a 1006a <<<<

I was going suggest you followed Miriams siblings lines and see if anyone knew, but that said, I cant see her birth, let alone siblings!

She went by the name of MEUX in 1911 and was only 17, so I doubt she'd been married - not impossible but unlikely

Might help get you started:

1911:
CHESTER, Henry Thomas Head Married M 24 1887 Baker Tunbridge Wells VIEW
CHESTER, Ethel Maud Wife Married
1 years F 25 1886 Orpington Kent VIEW
MEUX, Miriam Maid Single F 17 1894 Maid Domestic Folkestone VIEW
CHESTER, Thora Ethel Daughter F 0 (7 MONTHS) 1911 Feltham VIEW
RG number:
RG14 Piece:
6730 Reference:
RG14PN6730 RG78PN335 RD126 SD1 ED6 SN40

Registration District:
Staines Sub District:
Sunbury Enumeration District:
6 Parish:
Feltham

Address:
42 High St Feltham County:
Middlesex

Can anybody help me?!!! Miriam Meux would have been my great-grandmother. She had my Grandmother out of wedlock and subsequently fostered. Miriam went back for her when she was about 2 to take her to America with her but unfortunately my Grandmother didn't want to leave her foster parents so Miriam left her in England. I don't know anything about her but can only assume she was in service in the South-East of the UK. I know nothing more than that. Did she go to America and marry and have a family, was she married before she left, did she indeed leave England? Please, anybody out there related to me? It's been many years, my mother has never wanted to persue her family history but now at the age of nearly 70 has decided she might like to know!!!!