[1] During the Second World War, in the spring of 1941, Neame was commander of British troops in Cyrenaica (north-eastern Libya), recently conquered from the Italians by General Richard O'Connor.

During the First Battle of Ypres in October 1914, Neame experienced first hand in the trenches the inferiority of the British issue hand-grenades compared to their German equivalent, and set about creating an alternative, the sappers improvising rudimentary but effective hand grenades made from empty jam tins filled with scrap metal, with the charge being created using gun-cotton, and a cord-fuse projecting from the end of the tin, requiring ignition by flame.

[6] Neame was 26 years old when the following deed took place, for which he received the Victoria Cross (VC): For conspicuous bravery on the 19th December, near Neuve Chapelle, when, notwithstanding the very heavy rifle fire and bomb-throwing by the enemy, he succeeded in holding them back and rescuing all the wounded men whom it was possible to move.

[3][18] In June 1932 Neame was promoted full colonel[27] (skipping the substantive lieutenant-colonel rank) and became a General Staff Officer 1[28] in the Waziristan District in India.

[37] While Commandant at the Military College, Neame had been given to understand that should war be declared, he would be appointed as Chief of General Staff to the British Expeditionary Force's putative C-in-C, John Dill.

[40] In February 1941 Neame was appointed General Officer Commanding & Military Governor of Cyrenaica, which had been captured from the Italians by the British Empire's rapid advance in the opening moves of the North African campaign during Operation Compass.

The 2nd Armoured Division had only recently arrived from the British Isles, was under-strength, lacking in training and equipment adapted for desert warfare conditions, and proved to be no match for what it was about to meet in the field in the form of Nazi Germany's First Axis Offensive in North Africa, which was launched at the end of March 1941 by its newly arrived Afrika Korps, led by General Erwin Rommel.

With hesitant handling of his unprepared troop dispositions in response to a rapidly changing and unexpectedly threatening situation, as the Afrika Korps and Italian Army poured toward him at a terrific speed of advance and began on 24 March 1941 to attack his units' outposts and appear suddenly amidst, and even far behind them in the lines of supply routes,[43] and his command being limited in effective control by a Headquarters not sited in a battle station and remote from the action, Neame was over the next few days of fighting overwhelmed by Rommel.

Faced with the apparent danger of the 2nd Armoured Division's disintegration which he perceived from its chaotic radio-traffic as it struggled to cope with the rolling blows it was receiving, he ordered the forces under him to fall back eastward in an uncoordinated fashion to avoid being cut off and completely destroyed by the sudden advance of the enemy.

[44] Along with the almost 3000 men of the 2nd Armoured Division who had been captured in Rommel's advance, Neame with generals O'Connor and Combe were transported across the Mediterranean Sea for incarceration in Italy, first being held as prize prisoners at the Villa Orsini near Sulmona, then at Castello di Vincigliata PG12 near Florence.

Whilst at PG12 they took part in a number of escape attempts along with General Adrian Carton de Wiart (a fellow VC recipient), and Edward Todhunter.

Having hidden a manuscript which he had been writing in captivity of his memoires (to be recovered after the war), Neame's party, including Air Marshal Owen Boyd and General Richard O'Connor, made their way southwards with the help of friendly Italians along the route.

[46] Arriving back in England on 25 December 1943, having travelled via Tunis (after interviews with Generals Dwight Eisenhower and Harold Alexander, and also Winston Churchill), Neame found there was no job waiting for him in the army, with his star in the descendent after the debacle of his capture in 1941, but he remained on the Active List until the end of the war in his substantive rank of major-general.