Naming patterns if followed
First daughter Ann -- usually named for wife's mother, however John Wright's mother is also Ann!
second daughter Eleanor (aka Helen) usually named for his mother.
The 2 sons Adam and Peter are not named for him or his father, have you traced John Wright's family, are these the names in previous generations.
Do you have the newspaper clipping -3 May 1834 Northampton Mercury.
The three children of John Wright of Sulgrave were buried in one grave , they had been ill with some sickness for one or two days.
(Ann age 8, Adam age 4, Peter age 2 all buried 14 April 1834)
The name Ann meant a lot to them as on 25 December 1834 another daughter named Ann.