Hi Cate
I have pretty much the same as you -
Pigott, Samuel (of Sheffield, born 1837-04-14). Baptised May 7, 1837, by E Goodwin at Sheffield Parish Church, Church Street, Sheffield. Parents name(s) are Ann & Samuel (Joiner).
1841 Census I have Samuel & Ann , George,Harriett, Mary Elizabeth, Samuel Ann & Stephen at Allen st /Morpeth street
1851 Samuel Ann Mary Elilzabeth Samuel Ann & Charles at 28 Ct, 9 Granville Street
1861 Samuel Ann John James & Margaret all listed as Andersons at 20 WestJohn Street then on the next page is James Henderson at 20 West John Street
1871 Sam, Ann, John,Margaret Mary Herbert & ALice at 124 Solly Street - again as Andersons
1881 Samuel, Ann Margaret Mary Eliz,Herbert,Alice Jospeh & Frederick at 150 Solly Street as Pigotts
1891 Samauel & Fred at 150 Solly Street as Pigotts
1901 Samuel Frederick Martha & Martha Pigott at 150 Solly Street
Death 1902 - The inscription on the headstone is Pigott too - cant insert it on here sadly
It seems that they adopted the Anderson surname and Henderson middle name for the children following his marriage to Ann Wilson. Maybe he found out that at that time that Samuel Pigott wasnt really his father or they had a fall out or something or maybe James Henderson was simply a border who signed their marriage certificate for some reaosn ?
I didnt get the pic of the marriage certificate but if you could send it outside of this website to
di.neal1@btinternet.com that would be great and I will send you pics I have of all the Pigotts headstones .
maybe between the 2 of us we can crack this mystery !

Di x