Torp had been a member of Sarpsborg city council from 1919 to 1923 and deputy member of Aker municipal council from 1925 to 1928 when he in 1930 moved to Oslo. He served as mayor in 1935 and 1936, and was elected to the Parliament of Norway in the 1936 Norwegian parliamentary election. By that time he had already become acting Minister of Defence in Nygaardsvold's Cabinet, filling in for Fredrik Monsen who was ill. He was then Minister of Social Affairs from November 1936 to July 1939, and Minister of Finance from July 1939 to March 1942. In April 1940 Norway had been invaded by Nazi Germany, and Torp was responsible for initiating the successful flight of the Norwegian National Treasury. After overseeing the start of the flight, he fled together with the rest of Nygaardsvold's Cabinet. In Åndalsnes he was injured in the foot during the German air raids. The Cabinet ultimately reached Tromsø where they embarked for England, where they stayed until the war's end. Torp was acting Minister of Defence from November 1941 to February 1942, and then the permanent Minister of Defence from March 1942 to November 1945, in Nygaardsvold's and Gerhardsen's First Cabinet. Torp was a former antimilitarist, and was imprisoned for five months in 1924 as he called for a military strike, but shed this ideology from the mid-1930s.