Luxton was born in the Falkland Islands and educated in the United Kingdom before moving back to the islands to manage his family's farm at Chartres. In 1982 Argentina invaded and occupied the Falklands for 74 days during which time Luxton was identified by the Argentine military junta as a potential troublemaker. Along with his wife, Patricia, and their children, Luxton was deported to the UK where he became notable for giving numerous interviews about his experiences with the Argentine military. Luxton and his family returned to the islands at the end of the Falklands War.