The Christmas War
Britain was not to be caught unprepared. Many British regularly painted President Mustafa Tlass as the "Arab Hitler", including Labour Party leader Hugh Gaitskell, lamenting that their French allies had clearly taken the path of appeasement.[1] If even Labour was calling him Hitler 2.0, the Conservative government of David Fyfe was even more uncompromising, quickly deploying its troops to the Syrian border. With an election year rapidly approaching (the last British elections were in 1957), the Fyfe Administration was already unpopular due to the cost and expense of several colonial campaigns. The polls predicted a hung parliament even though the British economy, increasingly integrated with the rest of Europe, was booming. The British military presence in Jordan was rather large due to Britain being the primary supporter of the Iraqi Royalists (as part of the Arab Federation of Iraq and Jordan, or AFIJ) in the Iraqi Civil War. In contrast, the Syrians were the primary supporters of the Iraqi Nationalists, especially after a suspicious assassination attempt on Nationalist leader Abd al-Wahab al-Shawaf killed the Nationalist leader.
The planners of the assassination was one of the most closely guarded Arab mysteries. Popular opinion generally blamed the MI6 of Great Britain since one could intuitively conclude that killing the relatively moderate al-Shawaf would eventually chase more moderates into the Royalist camp. In reality, the operation was undertaken by the United States Central Intelligence Agency, personally greenlit by President Kennedy, who judged that killing the moderate al-Shawaf would allow the Syrians to take control of the Nationalists, putting them on a collision course with North China. Indeed, this succeeded wildly, as the Syrians placed their own man in Iraq, Fuad al-Rikabi, in charge of the Syrian-supported Nationalists, as well as a local Iraqi millitant who worked with the CIA to enact the assassination, the 25-year old Saddam Hussein. The Nationalists and Communists immediately went to war in Iraq, further straining relations between Syria and North China. The radicalism of the Nationalists also chased away the Iranians, who had previously supported the Nationalists, but now simultaneously supported both the North Chinese-backed Communists and the American-backed Islamists. Indeed, this caused all three factions to unite against the Syrian-backed Nationalists.
In addition, Kennedy's ploy put the Soviets in an increasingly awkward position. The Soviet Union had received a naval base in the coastal Syrian city of Tartus to match the Soviet naval base in Port Arthur. As a result, it was forced to juggle its two ostensible allies, who loathed each other. Interestingly, Beria's lesson from the Three Years War was that the massive Soviet army was not as useful as the Soviets originally believed. However, he was consistently angry at the weak state of the Soviet Navy, which generally was unable to stand up to the Western powers in the Three Years War. Although able to prevent any NATO navies from entering the Black Sea or too far into the Baltics, the USA quickly established total naval superiority in the Pacific theater and the Anglo-French similar superiority in the Mediterranean theater, with the unlucky Soviet submarine that poked into the Black Sea quickly tracked down and sunk. With much better information than most other politicians, Beria had judged that the Soviet economy was actually crumbling under Western blockade by 1957. The Soviet Union engaged in a massive naval buildup immediately after the end of the war, which took more urgency after the Soviets were defeated by both the Americans and the French in reaching space. Both naval bases were essentially strategically invaluable to the Soviets - and nothing pained Beria more than the possibility he might have to pick one of those bases.
In Damascus, the Syrian detente with their former colonial ruler, France, cynically took advantage of De Gaulle's natural fondness for former French colonies so that Syria could turn their attention towards the struggle in Iraq. In particular, the Syrians saw Britain as the main enemy. If Britain were to collapse, that would open not only Iraq, but also Jordan and possibly even Egypt (though even Tlass's second-in-command, Hafez al-Assad had to admit this was a pipe-dream). Moreover, it was hard to find a power more unpopular than Great Britain in the Mediterranean. Royalist Greece and Turkey both loathed the UK for its planned annexation of Cyprus. Italy was mildly annoyed by the annexation of Malta. The Kingdom of Yemen had its eyes on British-controlled South Yemen. An increasing crisis was brewing in Asia over Singapore. The Argentines still hadn't given up on their claims on the Falkland Islands. Ironically, Tlass was not interested in destroying Israel. In many ways, he used rampant antisemitism and hatred of Israel, including his history of war crimes against Israeli citizens to legitimate his rule. If he were to actually destroy Israel, this would actually be far less effective.
On the morning of Christmas, when many British troops and officers were attending Christmas services, almost the entirety of the Syrian People's Army bulldozed across the Syrian-Jordanian border. The Palestinian fedayeen rose up in Jordan against Anglo-Jordanian forces and the Gaza Strip (against Anglo-Egyptian forces). They were so numerous, that Jordanian and Egyptian forces were taken by total surprise, especially because many of those fedayeen fighters had fought with Egypt and Jordan in the 1948 Arab-Israeli War. Interesting, because the West Bank was so open in terms of terrain, most of the Palestinian fedayeen from the West Bank were operating in Jordan itself, not the West Bank. The Jordanians had expected an attack on the West Bank as a plot to "flank" Israel, but not an attack on Jordan itself. Crossing near Nasib, Syria, the Syrian People's Army quickly bulldozed the Jordanians, who had many troops uselessly stationed in the West Bank. The Jordanian supply system collapsed as the fedayeen, active throughout almost all of Jordan (half of Jordanians were Palestinians, who almost entirely sided with Syria) made it very difficult to supply Jordanian troops by land, forcing the British to airlift supplies.
The British had strong contingency plans and immediately moved British troops to fortify Zarqa, north of Amman on the Damascus-Amman road and home to the largest Jordanian army and air base in the country (making it simple to supply from the air). The British understanding was that Anglo-Jordanian forces could easily blunt the Syrian advance at Zarqa, at which point the Mediterranean Fleet and the Asian Fleet would bring reinforcements directly into the Red Sea to push the Syrians completely out of Jordan and possibly even to Damascus. However, the Syrians had another trick to play. A day after the Syrian invasion, the Kingdom of Saudi Arabia and the Mutawakkilite Kingdom of Yemen, announced solidarity with Syria. Unbeknownst to the British, the three powers had signed a pact to partition conquered territories. Syria would get almost all of Jordan, Saudi Arabia would get the coastal regions of South Jordan that used to be part of the Hedjaz Kingdom (which Saudi Arabia used to claim), and North Yemen would obviously get South Yemen. Saudi participation shocked the British since none of Britain's Saudi contacts was told of this - largely because the Saudi Royal Family was largely opposed, with only the relatively left-wing, nationalistic King Saud himself being a supporter. In contrast, the British had expected North Yemen to attack if Syria attacked, so their troops fared far better.
Saudi Arabian troops immediately assaulted the city of Aqaba on the south coast of Jordan. Although Jordanian troops resisted fiercely, Aqaba was across the desert and more or less impossible to supply from the rest of Jordan because of the Palestinian uprising. Control of the city remained contested, but the Saudi Arabians prioritized completely the ports with artillery fire, effectively rendering Jordan landlocked. The British were forced to aerially resupply Jordanian troops in Aqaba from Egypt, which hurt as the British plan was to aerially resupply North Jordan from Egypt. The Saudi Arabians had purchased several Soviet-made SAMs, such as the S-75 Dvina, that rendered the planned aerial resupply of North Jordan impossible once the Saudi Arabian Army established some sort of position in Aqaba. British troops were far better trained and equipped than the coalition facing them, but the extremely disadvantageous situation of the war meant that something had to change for Great Britain - and change fast.
Several possibilities opened up for Great Britain. First, they could sail the Mediterranean fleet to the coast of Syria itself and launch a diversionary attack. Alternatively, they could reinforce in Kuwait and try to blow their way across Iraq. Third, they could try to launch an amphibious assault across the Red Sea to reinforce Jordanian troops in Aqaba. Their choices narrowed significantly after the Israelis, currently in control of the Suez Canal (or at least one side, enough to deny passage to anyone), declared "armed neutrality" whereupon no navy ships would be allowed to pass through the Suez Canal. This was seen as incredibly suspicious, because of Britain's overwhelming naval superiority, this was seen almost entirely anti-British. And indeed, Israel had also been promised something.
At the United Nations, a condemnation of Syria, Saudi Arabia, and North Yemen failed in both the Security Council and the General Assembly. Not only did the entire Communist bloc vote no, but so did Brazil, Italy, Argentina, Turkey, Malaya, and (North) Greece (their UN seat was occupied by the Royalist government). Most disturbingly, several expected allies voted present, including Canada, Spain, Israel, France (De Gaulle feared an oil embargo), Ethiopia, India, the Philippines (South) China, and most devastatingly of all, the United States, which was a shock present vote. The message was clear: Britain would have to win this by herself.
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[1] OTL Gaitskell compared Nasser to Hitler - and Syria is far more extreme than OTL Syria.