If it is the 1851 family at Aston *** Aughton, also add child Hannah age 4 (= born about 1847).
I believe Rotherham is the registration place for Aston *** Aughton births.
With FreeBMD.org.uk and then gro.gov.uk we find births for Hannah June q 1846, Elizabeth March q 1844, & Eliza Dec q 1839 registered Rotherham and all matches have mother's maiden name Webster.
Can't locate a reliable Charles, and Sarah predates GRO.
You should further explore the Webster possibility.
Ancestry has 53 family trees for Thomas Hall & Hannah Webster, most with a marriage 1827 at Aston. Take these with a grain of salt, until you can verify, but it could be worth following up.
I don't know where in the world you are, but many libraries have the gratis library edition of Ancestry.
At the previously mentioned marriage of Thomas Hall and Hannah Webster on 26th November 1827 at Aston, the witnesses were George and Mary Webster.
In 1841 Thomas 37 and Hannah 33 were living at Aughton with children Joseph 1829, John 1831, Sarah 1832, Ann 1835, Charles 1837, Elizabeth 1840 and Thomas Lancaster 1837. Next door to them was John Webster 30, wife Rachel, children Mary 9, Hannah 6, Joseph 4, John 2, Sarah 4 months. John W was possibly a relative of Hannah?
To be clear:
Aston is the name of the ecclesiastical parish, and Aston *** Aughton is the civil parish. However, Sheffield Archives have this incorrectly in their catalogue of the church records, so Findmypast has the incorrect name from there.
The OS map of 1850 shows it correctly. https://maps.nls.uk/view/102345223