Nathaniel Greaves was born in 1787, the son of John Greaves, a cutler and Margaret, his wife. He was apprenticed to Joseph Parlebien Antt, a knife maker, in 1801.

He is listed in the New, General & Commercial Directory of Sheffield, 1825, as a merchant, table knife manufacturer and steel converter at 54 Coal Pit Lane. By 1828 he is operating from Portobello Street.

On the 1841 census, he is living with is wife Mary (nee Clarke) at "Shirley" in Ecclesall Bierlow (later recorded as Shirle Hill). At some point in 1850 or early 1851, the family moves to London although he continues to hold the property on Portobello Street, described as Freehold Warehouses in the electoral registers.  
On the 1851 census, Nathaniel is living at 38 Thurloe Square, Kensington and is recorded as a "Landed & house proprietor". It seems unlikely that he would still have any involvement in knife manufacture at this point.

Nathaniel died in Islington in 1856 and is buried in Highgate cemetery.