The following are the only clues to the Nicholsons, possibly these are Elizabeth's parents?:

The Crown and Dolphin, Kneesworth Street, Royston
(Royston & District Museum)
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John Nicholson was licensee of the Crown & Dolphin 1802 - 1805. {from "Royston Inns"}
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the license then passed to Jane Mary Nicholson 1806 - 1822. {from "Royston Inns"}
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Mar 30th 1806, John Nicholson, no age given, of Royston (possibly the licensee above). {Royston Parish Church burials 1800 - 1851}
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Aug 21st 1832, Jane Nicholson, 74 of Royston (possibly Johns widow). {Royston Parish Church burials 1800 - 1851}
The Nicholson family were probably from Aspeden is just south of Royston.
The IGI shows two records for births to John and Jane Mary Nicholson:
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MARY ANN NICHOLSON, Female, Christening: 02 SEP 1792 Aspeden, Hertford, England
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SOPHIA NICHOLSON, Female, Christening: 13 APR 1794 Aspeden, Hertford, England
ASPEDEN, a parish in Royston district, Herts; on the river Rib, 8 miles SE of Baldock r. station. It includes part of the Post Town of Buntingford. Acres, 1,351. Real property, £3,539. Pop., 577. Houses, 114. The property is divided among a few. The manor belonged to the Cliffords, the Freemans, and the Jocelyns; and passed to Earl Hardwicke and the Bolderos. Aspeden Hall and its park are a prominent feature. The living is a rectory in the diocese of Rochester. Value, £357.* Patron, the Countess of Mexborough. The church contains a curious monument to Sir Robert Clifford, master of the ordnance to Henry VIII., and other tombs and brasses; and is in good condition. An endowed school has £17 a year, and other charities £37.
It would seem very likely that Elizabeth, who was probably born ca 1785-1790, was an older sister of Mary Ann and Sophia.