He is considered the father of modern taxidermy. He introduced the style of dramatic preparation in taxidermy. One of his famous works "Struggle with the quarry" depicted a falcon attacking a heron which held an eel.
This taxidermy mount was an attraction at the 1851 Great Exhibition at the Crystal Palace in London.
Hancock was born in Newcastle upon Tyne and educated at The Royal Grammar School. He was a brother of the naturalist Albany Hancock.
His father was also a John Hancock and he ran a saddle and hardware business. He may have trained in taxidermy under Richard Wingate, a neighbour of Thomas Bewick.
Hancock was a mentor and tutor to the celebrated ornithologist and bird painter, Allan Brooks.
In 1874, Hancock published his Catalogue of the Birds of Northumberland and Durham. Hancock edited Thomas Bewick"s 1847 edition of Birds. In 1868 he planned a layout for Newcastle Town Moor, which was only partly realised.
In 1875 he was asked to prepare a plan for Saltwell Park, but declined due to pressure of work.
The Hancock Museum in Newcastle upon Tyne is named after the Hancock brothers, both of whom took an instrumental part in getting the museum built. The museum contains many specimens from their collections.