He began his theatrical career acting in repertory in Ireland, later joining Charles Doran's Shakespeare company.
Dudley created Dr Morelle for a BBC Radio anthology programme Monday Night at Eight during the Second World War.
He featured the character in many short stories and numerous novels as well as a stage play Dr Morelle, which he co-wrote with Arthur Watkyn.
He appeared in the West End in numerous small parts, before taking a job with The Daily Mail during the late 1930s as a society reporter.
His popular radio series The Armchair Detective attracted more than ten million listeners a week.