I can find Thomas COX and Eliza on the 1861 census - High Street, Tewkesbury

1861 - Eagles Alley

Thomas COX - 38 - born Churchend
Eliza - 35 - born Poundhope (there are a few people on later census born Pound Hope, which is Herefordshire)
Harriet - 9 - born Hereford
Louisa - 7 - ditto

? Do you have the birth certificates of Harriet/Louisa, which would give the mother's maiden name

???

England & Wales, Freebdm

Name: Louisa COX

Date of Registraton: Oct-Nov-Dec Qtr 1854

Registration District: Leominster

Inferred County: Herefordshire

Volume: 6a

Page: 441

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Can't see Thomas & Alice on the 1871 census, could you provide this? to see where Alice was born.

Checked the Gloucestershire baptism index - no Thomas COX christened at Churcham - and no other Cox baptisms or marriages at Churcham.