Thomson's father, also called Alpin Thomson, was a colonial administrator in Western Australia at the time of his birth, being under-secretary for railways in the colony's government. His mother was, in one account, the daughter of the colonial secretary (equivalent to chief minister) of Western Australia from 1877 to 1880, Sir Roger Goldsworthy, and Goldsworthy left Alpin Thomson Sr and his wife with his unfinished house, called Lucknow, at Claremont, when he was posted to St Lucia in 1881. In 1933, Thomson's mother was cited in "The Times" as one of just nine remaining survivors of the Siege of Lucknow in 1857; if that is accurate, it explains the name of the house, but she is likely on grounds of age to have been Goldsworthy's step-daughter rather than a direct descendant. By the time of the First World War, Thomson's parents had retired to live at Wellington, Somerset.