What I now have on William Allingham (b. c. 1785) is: The Biographical Index of South Australians (1836 to 1885 CD) names William Allingham, b. c1785 in Kent, England; (notedifference here- but I think the Dorset data is more accurate) d: 12.9.1873 Mt Barker Springs (Residence Nairne) 88yo; bd: Nairne.  He was a Gunsmith and lived at Under Mount, Nairne, Sth Australia.  m. (c 1800) Elizabeth [NN].
The 1861 Census of England lists a person of same age and name (b. abt. 1785, at Aldgate Middlesex) living at 1 Queen St, St Botolph Without Aldgate, with his unmarried daughter, Jemima Cole aged 46yr also b. Aldgate, Middlesex.Ref. RG 9/274 p. 17.
William Allingham may be same person, b. 27 Apr. 1785, St Leonards, Shoreditch, London, baptised 14/12/1798, Shoreditch. LDS ref. CO40801 0396230; 0396231: Parents Thomas and Mary Allingham.
ALLINGHAM William, emigrated to Sth Australia, aft. 1861, date unknown.
References  South Australians 1836 to 1885 CD, BISA Vol1., p.20, ALLINGHAM William b: c1785 KEN ENG d: 12.9.1873 bd: Nairne SA occ: Gunsmith res: Under Mount, Nairne m: unknown ch: Sarah DALTON (1811-1898).
He may have had a daughter named Jemima, sister to James (b. 4th Aug 1811- the ancestor of William Jones) and Sarah (b. 1811 ? who married John Dalton).
Susannah Arrington/ALLINGHAME is a possibility (given that the records probably are not in her hand or that of her husband and an English accent could distort names (as I have discovered in other cases involving records).
I am now trying to match in the two implied Allingham lines- James to Jane to Bill Jones; the other from James and Joyce to Susannah Arrington/Allingham.I will get back.It turns out a bit incestuous if both lines converge in the union of Maggie and Bill and have a common ancestry.