Thank you Rolnora, Radcliff, and Lancsann.
Benjamin Carrington was born in 1776 in Hampsthwaite Yorkshire. He married twice, secondly to Ann Longley Booth on 18 May 1807 St Peters, Leeds. The eldest son of this second marriage was Peter (1807-1886), who was my ancestor.
Some time between 1813 and 1816, Benjamin, Ann and family moved to Liverpool; I assume this would have been for work purposes. With the help of the excellent Lancs OPC site, I have discovered they had more children in Liverpool. Peter was put on trial for stealing some brass, and was transported to Tasmania. On receiving his freedom, he came to South Australia, and settled down.
It is their life in Liverpool that I am piecing together at the moment, and Benjamin's death is the first piece of the puzzle.