During the Second World War, Kirkman served initially as Commanding Officer (CO) of the 65th Medium Regiment, Royal Artillery, a second line Territorial Army unit, which in 1940 was sent overseas to France to join the British Expeditionary Force (BEF), where it fought in the Battle of France, only to evacuated at Dunkirk. He was made an Officer of the Order of the British Empire (OBE) on 1 January 1941. He remained with the regiment until being promoted to acting brigadier on 23 March 1941 and being made Commander, Royal Artillery (CRA) successively in the 56th (London) Infantry Division, I Corps, VIII Corps, XII Corps and South-Eastern Command. Both XII Corps and South-Eastern Command were led by Lieutenant-General Bernard Montgomery, who came to form a very high opinion of Kirkman. Kirkman's rank of lieutenant colonel was confirmed on 22 May 1942.