There are a number of well known portraits of James Cook and one of his widow, Elizabeth, as an elderly lady. The latter is in the Mitchell Library, State Library of NSW (call number ML 430).
Elizabeth was born on 31 January 1742 to Mary (nee Blackburn) and Samuel Batts. She had two siblings – Sarah and Samuel. Her father was the inn keeper of the Bell Inn, Wapping, England. James lived at the inn as a young man and Samuel mentored James. Elizabeth and James married on 21 December 1762 at St Margaret’s Church Barking Essex. She was 20 and he was 34.
Elizabeth and James had six children – James (1763-94), Nathaniel (1764-80), Elizabeth (1767-71), Joseph (1768), George (1772) and Hugh (1776-1793), all of who predeceased her.
Elizabeth lived in the East End of London until 1788 when she moved to Clapham, Surrey.
She was noted as a needle woman and an example of her work is in the Mitchell Library, Sydney. She died on 13 May 1835 aged 93 years and was buried at St Andrew the Great Church in Cambridge with two of her sons. She outlived her husband and each of her children and left no known descendants. She left gifts to the minister of the church, to support the family monument and for poor aged women. She destroyed all of the personal letters to her from her husband. She strongly supported her husband’s reputation and her keenest expression of disapprobation was “Mr Cook would never have done that!”
The portrait of Mrs Elizabeth Cook is said to be of her at the age of 81 years and signed “W. Henderson.”
There are two identified artists in England in the nineteenth century with the name “W Henderson.” These are William Henderson 1874-1892 of Whitby and W P S Henderson of 1836-1874 of London. Neither, were therefore painting either in 1830 or before the death of Mrs Cook. This does not preclude that the portrait was by one of these artists who painted from another painting or drawing. 
The portrait was given in 1956 to the Mitchell Library by Mrs H J A Chorley following the death of her husband, Henry Chorley, who was the son of William Chorley of Cheltenham and the son actively involved in W Chorley & Co Pty Limited – the tailoring business of William Chorley. The portrait used to hang, with 8 others, in the George Street showroom of W Chorley & Co. This is the Cheltenham connection.
The 8 other portraits are described in the Library archives as the Yorkshire ancestors of F Thornbury of Sydney called Dale & Reynolds. All of the painting were originally offered by way of loan to the library by Henry Chorley in 1938 however the Trustees declined a loan and indicated that they would only accept a gift.
It is possible  that the paintings came from an auction on 10 August 1905 of the estate of David Featherby Thornbury which was described as including “… Water Colour drawings, and oil Paintings including some Fine Old Family Portraits. Also a Small Collection of Books including Old and Rare Australian Works.”  Mr Thornbury was a barrister and died at his residence “The Bungalow” Titania Street Randwick in his 80th year on 29 May 1905.  He died intestate and the curator of the Estate said that he was known as either Featherby David or David Featherby Thornbury. 
A 1905 purchase date means that the purchaser was most likely William Chorley – whose biography appears elsewhere in this web site.
 There is another possibility because the widow of David Thornbury Agar of Whitby England lived at Carlton House 521 King Street Newtown from at least 1900 until her death in 1913: see the marriage notice of her daughter Rose in Daily Telegraph 13 January 1900 page 1, and her death notice Sydney Morning Herald 1 September 1913 page 7. There is no record of this person having any paintings.
 Evening News 5 August 1905 page 3
 Sydney Morning Herald 30 May 1905 page 6
 Government Gazette of the State of New South Wales 22 August 1905 page 5708.