Born in Chelsea, London, on 28 April 1907, the son of Colonel Sir Neville Anderson, Anderson was educated at Tonbridge School and the Royal Military College, Sandhurst. After passing out from Sandhurst, he was commissioned as a second lieutenant into the King's Own Royal Regiment (Lancaster) on 1 September 1927. Anderson served with the 2nd Battalion, King's Own throughout most of the interwar period and was promoted to lieutenant on 1 September 1930, and captain on 28 December 1936. From 30 March 1937 he served as his battalion's adjutant, which was deployed to Palestine the following year, where it was stationed during the Arab revolt in Palestine, and commanded for most of this time by Lieutenant Colonel Neil Ritchie, who was succeeded in August 1939 by John Hardy. For his services in Palestine Anderson was mentioned in dispatches on 15 September 1939.