[2] During the First World War, Kirkman joined the British Army and, after passing out from Woolwich, was commissioned as a second lieutenant into the Royal Artillery on 10 February 1915.

[2] His fellow students there included several who would later achieve high rank in the future, among them Brian Horrocks, Cameron Nicholson, Nevil Brownjohn, Thomas Rees, Bertram Cripps, Frank Simpson, Keith Arbuthnott, Arthur Dowler, Joseph Baillon and Ian Jacob.

He then completed a two-year staff posting to the Royal Air Force (RAF) School of Co-operation in January 1938.

[17][18] 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, along with most of the rest of the BEF.

Both XII Corps and South-Eastern Command were led by Lieutenant-General Bernard Montgomery, who came to form a very high opinion of Kirkman.

[21] In August 1942 Montgomery was ordered to take command of the British Eighth Army in the Western Desert in North Africa.

[20] Almost forty years later, Kirkman remarked upon this particular incidence to Nigel Hamilton: "I mean if one looks back, almost any other Commander in history, having attached importance to an event of that sort would probably have said 'Is everything all right − are you happy?'

Quite extraordinary from my point of view..."[23] The fire-plan for Operation Lightfoot required the field artillery of Sir Oliver Leese's XXX Corps, which contained five infantry divisions, and Herbert Lumsden's X Corps, with two armoured divisions, along with three medium regiments, which were then the only ones deployed in the theatre.

The operation's second phase was to consist of a creeping artillery barrage, which was to move ahead of the advancing infantry and lift at a specific time.

Although the Axis positions had so far suffered very heavy losses, and their defences had been battered, the armoured divisions of Lumsden's X Corps were unable to break through into the open country beyond, thus necessitating more infantry attacks.

[25] In the next few days Montgomery launched a new assault, Operation Supercharge, which was accompanied by a massive barrage of some 360 guns, all from Leese's XXX Corps.

[24] The pursuit of the retreating Axis forces now began, and Kirkman was critical of the speed with which the Eighth Army, in particular Lumsden's X Corps, pursued them.

The division − understrength with only two infantry brigades (69th and 151st) instead of the usual three − was a first line TA formation with extensive experience and was then engaged in the final stages of the Tunisian Campaign, serving in the Eighth Army's X Corps, then commanded by Lieutenant General Brian Horrocks, who had been one of Kirkman's fellow students at the Staff College in the early 1930s.

[24] Kirkman led the 50th Division to Enfidaville it was relieved by elements of the newly arrived 56th Division, and was withdrawn into Eighth Army reserve, later moving to Egypt, where it commenced training in amphibious warfare, having been selected for participation in the Allied invasion of Sicily (codenamed Operation Husky).

Kirkman's division was, by the time he became GOC, a highly experienced formation, having served in France and Belgium in 1940, in the Middle East from 1941 to 1942, and in many battles in North Africa in 1942 (there losing its 150th Brigade).

After the Sicilian campaign was over the division was sent to the United Kingdom to prepare for the Allied invasion of Normandy, planned for the spring of 1944.

[31] Shortly before the relatively brief Sicilian campaign ended Kirkman was, on 5 August 1943, made a Commander of the Order of the British Empire (CBE).

[32] In mid-January, however, Kirkman handed over the 50th Division to Major-General Douglas Graham and received orders to proceed to Italy to succeed Lieutenant-General Miles Dempsey, who was to return home to take command of the British Second Army, with Kirkman succeeding him as GOC XIII Corps.

[37] XIII Corps, under Eighth Army, played a key role in the fourth and final battle of Monte Cassino in May 1944 and later came under command of the U. S. Fifth Army, under Lieutenant General Mark W. Clark, fighting on its right wing in the assaults during the autumn and winter of 1944 on the Gothic Line and central Apennines.

[38] XIII Corps later returned to Eighth Army command in January 1945 but Kirkman himself, whose rank of lieutenant general was made temporary on 20 January 1945,[39] was invalided back to the United Kingdom with severe arthritis in March,[40] command of XIII Corps going to Lieutenant General Sir John Harding, formerly Alexander's chief of staff.

[42] He was promoted to full general on 22 August 1947,[43] He was appointed a Knight Grand Cross of the Order of the Bath in December 1950.

He retired to Hampshire where he died on 29 October 1982, aged eighty-seven, over forty years after the Second Battle of El Alamein in which he played such a vital, if relatively unknown, role.