There is a Henry Talbot b 1851 durham central in the online Durham GRO certificate orders.
1861 census Shotton - is this grandson this Henry
1861 Census, Easington District
Family Number: 2751.6
Shotton 1861 Census, Shotton Colliery, First High Row
Henry Tarbitt [Tarbutt], Head, married, 57, Colliery Engineman, born Wooler, Northumberland
Frances Tarbitt [Tarbutt], wife, married, 57, born Wooler, Northumberland
George Tarbitt [Tarbutt], son, 20, Enginewright, born Easington, Durham
Frances Tarbitt [Tarbutt], daughter, 13, Scholar, born Easington, Durham
Henry Tarbitt [Tarbutt], grandson, 9, Scholar, born Easington, Durham
1871 grandson aged 19 at Shotton
Frances Black
23
Harwell, Durham, England
Daughter
Shotton
Durham

Frances Black
1
Castle Eden, Durham, England
Granddaughter
Shotton
Durham

Henry Black
3
Castle Eden, Durham, England
Grandson
Shotton
Durham

Frances Tarbit
67
Ford, Northumberland, England
Wife
Shotton
Durham

Henry Tarbit
67
Wooler, Northumberland, England
Head
Shotton
Durham

Henry Tarbit
19
Haswell, Durham, England
Grandson
Shotton
Durham
1881 census 23 Wynyard St Stockton
Henry Tarbit (Farbit)/H/M/19/Engine Fitter/DUR Haswell
Mary J/Wf/30/So Hetton
Maggie E/Dau/Unm/3/Stockton
Frances M/D/Un/2/Stockton
Georgina I/D/8 mos/Stockton

1891 census at Westoe St Shields 81 Stanhope Rd
Henry Tarbit/H/M/38/Engine Fitter/b Haswell
Mary J/Wf/M/40/South Hetton
Maggie E/D/13/Scholar/Stockton
Frances M/D/12/Scholar/Stockton
George H/S/6/Scholar/Stockton
Emily/D/3/Newcastle

At 33 Mill St, Norton Durham in 1901 census
Henry Tarbit/H/M/49/Haswell
Mary/W/50/NOT
Francis/S/22/Stockton
George Henry/S/Stockton
Emily/D//NOT
Wilhemina/D/3/Dur? So Moor? (sic)

1911 census Stockton Durham
11 Grange Terrace Norton Stockton-on-Tees
Henry/Head/59/Mar/Engine Fitter/b Haswell Durham
Mary Jane/60/mar for 37 years/b South Hitton C Durham
Wilhelmina/18/Dau/b South Moor Co Durham
Elizabeth Swinburn/Granddaughter/7/b Norton on Tees Co Durham