Robertson was the eldest son of Field Marshal Sir William Robertson and his wife Mildred Adelaide (née Palin), and was educated at Charterhouse and the Royal Military Academy, Woolwich.
With the outbreak of the Second World War, Robertson re-entered military service in 1940 as a temporary lieutenant colonel in the South African Army, and served in East and North Africa, and Italy until the end of the war, notably as Harold Alexander's Chief Administration Officer in Italy.