 When sitting United Australia Party (UAP) MP William Foster died in office, Robson stood as an Independent UAP candidate at the resulting by-election in Foster's vacated Legislative Assembly seat of Vaucluse.At the by-election on 29 August 1936, he emerged successful, with 62.63% of the vote, becoming the third generation of his family to serve in the NSW Parliament.Soon after his election Robson joined the UAP but soon joined a group of government backbenchers who were unhappy with the Bertram Stevens government's economic management and the party's control over preselection, becoming prominent in the struggle that led to the resignation of the Premier Stevens and his replacement by Alexander Mair in August 1939.