In 1814, a "John Needham of Hargate Wall, parish Hope, co. Derby carrying on business at Litton-Mills, parish Hope aforesaid, cotton-spinner" was listed as Bankrupt.
And again in 1835
Death notices:
Notts Review 25 May 1827
On the 11th inst after a protracted and painfull illness, aged 49 , Mrs Needham relict of the late Mr John Needham of Hargate Wall, nr Tideswell
Manchester Courier 27 April 1866
April 23rd in his 79th year, John Needham Esq formerly of Hargate Wall Derbyshire
So if the bankrupt John Needham is the same as the one who died in 1866, he cannot be a son of John & Olive, but possibly from an earlier marriage of John Neeedham snr?