Theer are a few William Cooper "suspects" in the 1841 but none a "strong enough" match so far ...

Possible, which would indicate a Non-conformist family which is why you are probably having difficulty with the BMD registrations around 1855 ( not compulsory then )

WILLIAM COOPER
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Event(s):
Birth: 28 JUL 1817
Christening: 15 FEB 1818 Independent-Nc, Little Dean, Gloucester, England
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Parents:
Father: JOHN COOPER
Mother: MARY
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Messages:
Extracted birth or christening record for the locality listed in the record.
The source records are usually arranged chronologically by the birth or christening date.
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Source Information:
Batch No.: Dates: Source Call No.: Type: Printout Call No.: Type:
C036141 1803 - 1837 0595449 (RG4 766) Film 6911875 Film