OK, the 1861 seems to match her PoB, allowing for a small mistran both by the Enumerator and the modern transcription.
1861 census of Dagenham, Essex RG9; Piece: 1069; Folio: 50; Page: 17
Charles Free 34 Head of Household born Cambs 'Harheath': an Ag Lab
Mary Ann Free 30 Wife Cambs, West?michter?
Eliza Free 16 dau Cambs, 'Horheath'
Agnes Free 14 dau ditto
Judith Holdle Free 4 dau ditto
George W Free 7 son Essex, Barking
Thomas Alfred Free 11Mo son Essex, Dagenham
Isaac Foster 26 Lodger born Essex, Hempstead
Look closely at the Foster Lodger - his PoB matches Solomon's in 1871 ! Mabe a relation?
Also, I'd wager this is a 2nd marriage for Charles given Mary Ann's age and the kids ages ...
In 1851 census of Horseheath, Cambridgeshire HO107; Piece: 1761; Folio: 353; Page: 22 - Eliza is a Visitor in the Household of John Free - I'm guessing that he is her Uncle ....