Based on how they are listed in 1841 Thomas age 1 and William age 2 months are the children of
Elizabeth Oxberry nee Jordan/Gordan wife of William Oxberry.
1851 Census they are in St Lawrence Parish York, Regent Street Thomas 11, William 10, Mary Ann 5, James 3, George 1.
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GRO Index says mother's maiden name for Thomas is Gordan, for William it's Jordan, Mary Ann it's Jordan.
Haven't found James as yet but George is reg. York 1850 as Oxberey, mother's maiden name Jordan
They also had a daughter Sarah 1843 reg. Sunderland, death reg. Stockton 1847 age 3
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William Oxbury married Elizabeth Jordan 20 January 1840 in Billingham.