Fred, that family you specified in the 1851 census is in the 1861 census in Nottingham and in the 1871 census in Nottingham. William H is still there in 1861 but gone in 1871. The family is very large, and ELIZABETH's parents (surname CHURCH) are with them in 1861. Her mother age 90 is still with them in 1871.
The GRO index shows the births of all the children (except Elizabeth 1848) with mother maiden name CHURCH.
Dave
Edit Elizabeth Church married William Lindley in Q2 in Nottingham in 1845.

Fred, Elizabeth Ann Lindley mother maiden name Church born Nottingham Q1 1849. Looks like she died Ecclesall Bierlow Q2 1851.
Dave

Hi Frederick,

William Lindley married Elizabeth Church, 8 May 1845 at St Paul,
Nottingham.

Moira.

Fred,

This is a baptisms for Sheffield that might be of help.

lindley, william (of sheffd, born 1823-01-31).
Baptised March 2, 1823, by M Preston at Sheffield Parish Church, Church Street, Sheffield.
Parents name(s) are jane & george (Snuffer Mkr).
Note:
Godparents: :Page No 263 :Reg No 2100

Elaine in Ottawa.

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HI , just a shot in the dark from me BUT if some of your LINDLEY"s are connected as my sample then its the same LINDLY line connected to my family
1 william lindley born about 1807 wife elizabeth (mappin)
2 selina lindley born about 1852 married william marshall had a daughter ada (my family line) , if they are the same lindley"s email me i may be able to offer a gedcom