I think you have the right man, but I don't think he dies in 1856.
In 1851 the Hardy family are living in Whickham. Two pages away is a widowed Ann Taylor, 48, b. Whickham, with a 10 year old son Peter, b. Whickham.
There is a death of an Elizabeth Hardy, age 51, abode Whickham in June qtr 1851.
There is a marriage of a John Hardy in Newcastle June qtr 1852, one of 2 possible brides is an Ann Taylor.
1861 census, Wood Houses, Crook and Billy Row,
John Hardy, 58, Brick Manufacturer, b. Brampton,
Ann Hardy, wife, 58, b. Whickham,
Peter Taylor, son in law, unm, 20, Brick Manufacturer, b. Whickham,
Mary A. Hardy, niece, 12, b. Brampton,
RG9/3715/5/4
1871 census, Tow Law,
John Hardy, head, 68, Engineman Colliery, b. Farlam, Cumberland,
Ann Hardy, wife, 68, b. Whickham,
RG10/4953/42/4
1881 census, 35 Joiceys Tce West, Oxhill, Kyo,
Henry Hardy, 36, Coal Miner, b. Farlam, Cumberland,
Hannah ", wife, 35, b. Farlam, Cumberland,
Robert ", son, 4, b. Kyo, Durham,
Mary A. ", dau, 1, b. Kyo, Durham,
John ", uncle, wid, 78, Retired Brick Maker, b. Farlam, Cumberland,
Hannah ", mother, unm, 58, b. Farlam, Cumberland,
Thomas ", brother, unm, 24, Coal Miner, b. Farlam, Cumberland,
RG11/4943/35/8
Henry Hardy is a grandson of Thomas and Hannah Hardy, living with them in Farlam in 1851 and 61.
John Hardy marriage cert to Ann Taylor should confirm his fathers name.
Alan.