-You have the marriage ref but not the certificate??
-You don’t say what information is on any of the NZ births to William & Lucy
There should be a lot, and they would have given it. Not a third party who got it wrong.
Are they consistent over all the births.
However… the image for the marriage is on Ancestry. If you don’t have a sub, your local library probably does.
William Parlett Lucy Grand marriage was at Shouldham Thorpe, Norfolk 18th October 1873
Both resident Shouldham Thorpe
Wiliam’s father = Samuel, labourer
Witnesses Susanna Parlett & John Claydon
Everyone signed.
1871 Shouldham Thorpe
Samuel Parlett 72 born Marham
Sarah Parlett, wife, 70, Fincham
William Parlett 29, Shouldham Thorpe
https://www.familysearch.org/ark:/61903/1:1:VFNP-KJTSamuel Parlett & Sarah Porter married at S.T. 1826
They signed with their mark. A witness is Mary Ann Parlett.
Easily seen in censuses. Quite a large family.
1861.
https://www.familysearch.org/ark:/61903/1:1:M7NJ-R581851
https://www.familysearch.org/ark:/61903/1:1:SG64-XRM1841
https://www.familysearch.org/ark:/61903/1:1:M791-9FS. (A Porter on there)
Samuel & Sarah still alive in 1881
https://www.familysearch.org/ark:/61903/1:1:Q278-XTW6Williams birth reg
PARLETT, WILLIAM PORTER
GRO Reference: 1842 M Quarter in DOWNHAM UNION Volume 13 Page 85
You can buy GRO certs as a Jpeg instant download for £2.50
Edited after first posting.