If you trace this family down from this
https://www.tribalpages.com/tribe/brows ... onnections
You will find Census records are various versions of surname but mostly Hadlington or Adlington but it appears site started off with Haddleton and most records followed suit rather than putting what was on Census.
When GRO became available it was obvious that main version on GRO was Adlington
I have records to add from 1901 to 1911 Census and Canadian Census for 1916 and 1921 and all children were registered as Adlington but George Haddleton
https://www.tribalpages.com/tribe/brows ... ver=633658 is on bcc as Haddleton whilst Census and marriage records are either Hadlington or Adlington and gro record of children are Adlington and his marriage is as Adlington