Hi Debbi
I would stress the importance about obtaining a marriage certificate for Henry and Harriet which would give you more information regarding Henrys father.
I have noted the following information regarding the marriage of Charlotte and Thomas Cuff, but don't want to send you off on a red herring if this is not the family of your Henry.
Thomas Cuff = Charlotte Elizabeth Morris 5th November 1860 at Harworth, Notts.
Thomas Cuff, 40 batchelor, labourer, Oldcoates, father John Cuff, labourer
Charlotte Elizabeth Morris, 37 widow, housekeeper, Oldcoates, father John Cummins, labourer.
In 1861 Henry is living with Thomas & Charlotte Cuff, in Carlton in lindrick with Elizabeth 12 and George 3.
I have noted that George died in 1868 as George Morris Cuff
In 1851 Charlotte Cumming 24, is living with George Morris, 71, widower in Worksop. He comes from Torworth, Notts. (Not far from Worksop) along with Elizabeth Ann born 1848
Should this prove to be the right Henry then there is a birth registered in Worksop in the first quarter of 1854 of a Henry Morris.
As I say, I hope this is of help and not a red herring.
D Orris