If his fathers name is George on the marriage cert, then the William born York in 1843 is likely the right one as this George Duncan, or George Sedgewick Duncan on some records, was an Engine Fitter.
Can't see any connection between the two Duncan/Donkin families, other than a lady who fits the bill for being William born York's mother appears to be living in Winlaton in the same house as William Donkin in 1861, the unmarried Chain Maker from 1871 and 81.
1861 census Winlaton.
Ann Donkin, wid, 36, b Derby, Derbyshire
William Donkin, son, Unm, 37, Blacksmith, b. Winlaton
I'm wondering if there was some confusion, William can't be Ann's son, so maybe there was another William Donkin in the household who actually was her son.
I can't find this Ann after 1861, but there is a death of an Ann Donkin aged 38, Sep qtr 1861, Gateshead, so that could be her.
George Duncan married Ann Maddocks in Derby 1841, George an Iron Turner, as was his father William.
In 1841 census in Derby, William is an Engineer, George is a Fitter, whole family Not Born in County. George Duncan baptized Tynemouth 1823, son of William Sedgewick Duncan and Mary Ann McIntosh. All of his brothers and sisters were baptized in the Tynemouth and Longbenton area.
William Sedgewick Duncan, born Longbenton 1795, son of George Duncan and Mary Sedgewick.
In 1851, Ann Donkin, 27, born Derby City, and son William, 8, born York City, are in Stockton on Tees. William Sedgewick Duncan and family have also moved to Stockton on Tees.
A George Sedgewick Duncan, assumed father of the William born York, can be traced through to 1881, with a new wife Martha/Margaret Brown, can't find a marriage for them, and daughter Mary, b. 1850 Lancaster. Working as an Engine Fitter in 1861 and 1881.
So the connection is maybe that Williams mother Ann, from Derby, was living as common law wife of William Donkin of Winlaton, and the surname was just a coincidence. That would make George in 1881 census the Step Great Nephew of Robert and Isabella Forster, or something like that.
Alan.