There appear to be three Elizabeths (and not enough Thomas entries!). The Elizabeth Nottley on freebmd could be any of them.
Samuel and Mary (nee Stevens) Notley married in 1836 and had children in Wilstead; their first child, in 1837, was Elizabeth.
1841: Wilstead: Samuel Knotley, 24, ag lab; b in county; not living with any family
1851: Wilstead: Samuel Nottley, 35, ag lab; Mary, 32; William, 12; Joseph, 10; b Wilstead
1851:Wilstead: Elizabeth Nottley, 12, (b Wilstead) is a nursemaid to another family
1861: Wilstead: RG9/992
Samuel Notly (indexed as Notty), 47, ag lab, b Strudbrook, Suffolk
Mary N, 40, wife, lacemaker, b Apthorn, Northants
Elizabeth N, dau, 23, lacemaker, b W
Joseph N, son, 20, b W
Henry N, son, 7, b W
George N, son, 3 b W
1871: Wilstead: Mary Nottley, 53, lacemaker, b Northants; Henry, 17; George, 13.
1841: Bedford Union Workhouse: Martha Nottley, 25, lacemaker; Henry, 5; Elizabeth 3; all b in county
1851: Wisbech Workhouse (Camb): Elizth Notley, 12, inmate, b Bedford
(why Cambridge? Anna Mary Notley, 21, governess, b Norfolk, is living in Wisbech, but no apparent connection).
1861: Luton: Elizabeth, 22, unm, bonnet sewer, b Bedford; Elizabeth, dau, 1
1871: Luton: Elizabeth Notley, 31, un, bonnet sewer, b Bedford; Elizabeth 11, Alfred, 3
1841: Bedford: Martar (?) Notley, 28; Thomas, 5; Betsy, 3; children b in county; mother b out of county
1851: Bedford: Thomas Notley, 15, (b Bedford) is an apprentice bootmaker
1881: West Ham
Thomas H(enry) Notley, 45, dock lab, b Wilstead, Bedford
(children Martha S(arah); Henry W(illiam))
The IGI shows Charles and Mary Nottley having children in Stradbrook (including Martha in 1813 and Samuel in 1814) before moving to Wilstead and having several more from 1816. It is not definitely the same couple, but the dates and history fit well. They seem to have married in 1803 and had children up to 1825.
The 1841 entries are a bit of a mystery with two Martha Nottleys having daughters b c 1838. The one in Bedford would seem to be Samuel's sister (with two illegitimate children). It is not clear how the Workhouse one is connected, if at all.
My guess is that the Thomas of the original posting is the illegitimate son (and brother to Elizabeth number 3) of Martha; Martha being the sister of Samuel.
We could do with finding:
a. Mary (Samuel's wife) + Elizabeth, William, Joseph. It is just possible that these are the same as the 1841 Martha, Thomas, Betsy; but it seems unlikely.
b. Thomas (+ Martha, Betsy) after 1841/51.
Richard