This is a review I found at the Stone Stone website for a book entitled Rashid Alii and the Golden Square at War". I was curious as to whether this account aligned with the narrative in the book you have read...
"Background
Although Iraq was technically independent at the beginning of WWII, by treaty it was in fact very much subject to British influence. The RAF maintained bases at Habbaniya (outside Baghdad) and Shaibah (near Basra) -- both were on the peacetime air route to India -- and retained tranist rights for troops.
In 1939 King Feisal II was only four years old, so the Regency had been established under Adb al-Ilah. (Note that there seems to be no standardized Western spelling for many of these names.) The Prime Minister was Nuri as-Sa'id who was pro-British but also very much a nationalist. Increasingly, however, power was being gathered by the pan-Arabist -- and fiercely anti-colonialist -- Rashid Ali al-Gaylani and a cabal of four colonels dubbed the "Golden Square".
Per provisions of the Anglo-Iraq treaty, Iraq broke relations with Germany in September 1939. By March 1940, though, Rashid Ali had become prime minister. Although he and the pan-Arabists had no particular love for Germany or Italy, they realized that in the prevailing world situation the Axis offered the best opportunity for support in achieving pan-Arabist anti-colonial political goals. Consequently, when Italy entered the war in June 1940 Iraq did not sever relations. Churchill was not amused.
In July 1940 an Indian brigade group from India was earmarked for movement to Basra to show the flag, but it was diverted to the Sudan for operations in Italian East Africa.
By December 1940 British demands for removal of Rashid Ali were increasingly strident, and in January he was replaced with General Taha el Hashimi, another pan-Arabist but rather more palatable to London.
Rashid Ali and the Golden Square conspired to regain power. On 31 March 1941, learning of a plot to arrest him, the Regent fled to Basra and gained refuge aboard a British warship. At the beginning of April the Golden Square seized power and installed Rashid Ali as "Chief of the National Defense Government". Churchill remained unamused.
Seeking to gain control of the situation, the British on 16 April informed the Iraqi government that, per treaty terms, British troops would be landing at Basra and moving through Iraq en route to Palestine. No objections were raised in Baghdad. The next day British troops arrived by air from Karachi to reinforce the garrison at Shaibah and cover Basra. On 18 April Indian 20th Infantry Brigade, along with HQ Indian 10th Division, arrived by sea at Basra from India.
On 27 April Rashid Ali declared that no additional British troops would be allowed into Iraq until the current formations had departed. British infantry began shuttling by air from Shaibah to reinforce Habbaniya; approximately 400 troops were airlifted north. That night the British ambassabor informed the Iraqi goverment that additional troops would be landing at Basra.
On the night of 29/30 April 1941 Iraqi troops surrounded the British base at Habbaniya.
Battle of Habbaniya
RAF Number 4 Service Flying Training School was located at Habbaniya inside a steel fence-enclosed compound along the Euphrates. This unit mustered:
Audax - 32
Oxford - 29
Gladiator - 9
Gordon - 8
Valentia transports - 3
Blenheim I - 1
Hart trainers - "a few"
Even by mid-1941 standards, this was a pitiful handful of useless junk.
For base defense Habbanyia fielded the 400 newly arrived troops (of 1st King's Own Regiment), a battalion of native levies ("mainly Assyrian, but including Arabs and Kurds"), and eighteen RAF armored cars. There were also wives and families of the garrison.
The Iraqi armed forces included four infantry divisions (one at Kirkuk watching the Kurds, two in Baghdad, and one south of Baghdad), a mechanized brigade (sixteen light tanks, fourteen armored cars, and two battalions of lorried infantry), four river gunboats, and sixty aircraft (miscellanous British, American, and Italian models).
Iraqi troops occupied positions on the escarpment overlooking the Habbanyia airfield, barely 1000 yards from the perimeter; this force eventually numbered some 9000 troops with 50 guns. Although no hostile action was initiated, the British commander, Air Vice Marshal H. G. Smart, was warned that firing would commence if aircraft attempted to take off.
Smart elected to take the initiative. At dawn on 2 May 1941 his aircraft attacked Iraqi positions on the escarpment. The Iraqis replied with AA fire and shelled the cantonment, while Iraqi fighters from Baghdad attempted to intervene. Despite the extremely vulnerable position of the base, the Iraqis attempted no ground assault.
Within 24 hours of taking action, the besieged British had the upper hand. Their antique flying machines controlled the air and their tiny ground force began to send out raiding parties. On the night of 5/6 May they attacked the escarpment and forced withdrawal of the superior Iraqi strength. By 7 May the siege of Habbaniya had ended.
Meanwhile
While the "battle" "raged", other events transpired. On 2 May Rashid Ali appealed to Hitler for armed support, and the Axis immediately began to make moves to assist the Iraqi revolt. During 5 and 6 May a "preliminary agreement" was reached between Germany and Vichy by which "three-quarters of the [Vichy] war material assembled in Syria under control of the the Italian Armistice Commission [is] to be transported to Iraq and the German Air Force granted landing facilities in Syria."
On 9 May Axis aircraft began to land on Syrian airfields. On the 13th the first German aircraft flew into Mosul and the first trainload of war material arrived from Syria in the same city. The next day Allied aircraft began raids on Axis aircraft on Vichy fields in Syria.
From Palestine, Habforce -- comprised mainly of British 4th Cavalry Brigade (newly motorized), plus elements of the Arab Legion and the Transjordan Frontier Force -- was organized and set out to relieve Habbaniya. It crossed the desert via the oil pipeline route (including some of the pumping stations, such as H3) but did not arrive at Habbaniya until 18 May, by which time the garrison had already lifted the siege.
Indian brigades continued to land at Basra and began to push slowly north.
On 19 May Allied forces at Habbaniya began a slow advance on Baghdad, still heavily outnumbered. Axis aicraft continued to arrive, including 12 Italian CR42s on 27 May. Axis air operations were, however, greatly hampered by lack of suitable quantities and grades of aviation fuel. On the 30th British troops from Habbaniya reached the outskirts of Baghdad.
Although the British forces were quite weak and Baghdad was held by an Iraqi division, Rashid Ali fled. The revolt collapsed and on 31 May an armistice was declared in Baghdad and a pro-British government took office. The remaining Aixs aircraft and ground personnel withdrew.
Aftermath
Largely due to its willingness to permit Axis aircraft to assist Iraq, the Allies invaded the Vichy Levant in June. Habforce turned around and participated in that campaign as well, following which its main components (redesignated 9th Armored Brigade, but without tanks) also managed to join the Allied invasion of Persia.
Iraq, now firmly under British control, declared war against the Axis early in 1943.
Rashid Ali escaped to Germany where, as a guest of the Fuehrer and rival to another guest, the Grand Mufti of Jerusalem, he spent the remainder of the war broadcasting to the Arab world and planning to regain power when German pincers from Egypt and the Caucasus finally met at the Persian Gulf. He survived the war and escaped to Saudi Arabia where he was granted asylum, returning to Iraq after the 1958 revolution. In more recent years various points of interest in and around Baghdad have been named after the WWII-era leader."
Interesting that Rashid Ali escaped any retributiuon for siding with the Axis. He was similar in this respect to the Thai leader who was re-elected after the war I believe.