Hi there,
Found Andrew ANESBURY's burial in South Australia in 1889.
https://www.genealogysa.org.au/ In searching for Andrew and for Margaret, in South Australia I have come across the following, which I think are likely to be relevant to Martin's family history.
I have not yet found any independent online resource confirming that Andrew came from 'England' or naming his parents.
A DOUBLE - DOUBLE WEDDING
https://trove.nla.gov.au/newspaper/article/207613397 Express Telegraph 18 March 1887
ANSBURY-FISHER and FISHER-ANSBURY by Reverend C MARTIN.
Margaret ANESBURY aged 26, married Charles Templer FISHER aged 27, on 16 March 1887, at the residence of Mrs E Fisher, Yanyarrie, Frome, Sth Australia, Margaret was the daughter of Andrew ANESBURY and Charles Templer FISHER was the son of Charles FISHER.
John James ANESBURY aged 28, married Martha Eliza FISHER, aged 25 on 16 March 1887 at the residence of Mrs E FISHER, Yanyarrie, Frome, Sth Australia. John James father was Andrew ANESBURY. Martha Eliza’s father was Charles FISHER.
And there’s
Eliza Maria Fisher ANESBURY, aged 19, daughter of Andrew ANESBURY, married William Henry HAYWOOD on 10 September 1887 at the residence of Mr COOMBS, Yongala, Clare, Sth Australia. William was aged 21 and the son of Henry HAYWOOD. The Ref no. is 152/831
Jessie Adeline ANESBURY was born 20 February 1888, at Yanyarrie, Frome, Sth Australia. Her parents were John James ANESBURY and Martha Eliza FISHER. Ref. 411/20
Death
Andrew ANESBREY, of Yongala, Clare, Sth Australia,a married man, died 20 October 1889, aged 61 years. The informant was William HAYWOOD, his son in law.
Burial
Andrew ANESBURY, of Yongala Cowie, death 20th October 1889 … see
https://www.findagrave.com/memorial/112189216/andrew-anesbury Death
https://trove.nla.gov.au/newspaper/article/207964248 Evening Journal 19 Dec 1901
ANESBURY
On the 7th December, at the Port Augusta Hospital, after a short illness, John James, the kind and loving husband of Martha E Anesbury, of Yanyarrie, aged 43 years, leaving a wife and six children to mourn their sad loss.
JM