The Holocaust is much less severe, and millions of Jews post-war in Europe want out of Europe, angry at the Holocaust and Stalin's treatment of them. Thus, nearly four million Jews have soon moved to Palestine, which becomes the state of Israel in 1948 after a second Arab revolt. The Israelis destroy the Arab armies which try to take back Israel, but the Israelis wisely decide to bury the hatchet with them while they can. Many Palestinians are allowed to stay, but with the large number of new Jewish arrivals, Jewish Israelis outnumber Arab ones at least 2-1. Others who choose to settle in Lebanon, Egypt and Jordan get some money out of it, if they choose to accept it. Most do.
The Royal Navy after WWII develops its carrier and amphibious forces, thinking that these rapid-reaction forces will allow them to maintain an effective deterrent in the decades to come. As part of this, Eagle, Ark Royal, Victorious, Implacable and Leviathan are built or rebuilt in such a way that they can be used a high-powered fleet carriers. Battleship Vanguard stays in the fleet for a few years to provide amphibious support, and spends far more time on active duty than in OTL. The Royal Navy still goes through extensive cutbacks, but the cuts trim the fleet down to a modern, fast-moving and powerful force.
Nasser still makes his play for the Suez Canal, only Nasser makes the mistake of naming the US among the enemies of the Arab world. This leads to Eisenhower not having the least bit of issue with the British-French-Israeli action to take back the Suez Canal. The Israelis take over parts of the Sinai, though areas which are heavily populated by Arabs are generally ignored just to keep problems to a minimum. The British decide to remove Nasser from the equation and have little trouble doing so, particularly after the Egyptian Air Force is wiped out by British carrier aircraft and the Israelis. Landings are made with the support of gunfire from Vanguard and her French counterpart, Jean Bart. The mission is successful, but the British decide putting a puppet in Cairo is a bad idea and leave the Egyptians to their own devices. They did get the message, however. The Suez is never battled over again.
Fearing both the Shah of Iran and the Saudi Royal Family, several of the smaller protectorates in the Middle East ask for protection from the British and the Americans, offering to ensure oil supplies in return. This passes with little difficulty. Arab nationalism still blossoms, but it turns harder towards Moscow, just making it easier to support the House of Saud and the protectorates. The Shah soon also joins into this alliance of sorts, fearing both Islamic fundamentalism and the Soviets and their puppets.
The vast violence in India post-independence causes fears of similar violence in Sri Lanka, which leads to Colombo asking the British to keep a garrison there as a protection force. Knowing that the route to Singapore is an important one, the British agree to this. By the 1960s, Colombo is a major base for the Royal Navy and its efforts in the Indian Ocean.
Singapore gets independence as OTL, but the Malayan Emergency, flaring violence in Vietnam and Indonesia make the tiny city-state somewhat vulnerable, which leads to the same request. As before, Britain wants to ensure sea lane access for its vessels, and agrees to assist Singapore.
The economy of Britain recovers strongly though the 1950s, particularly as the energy supplies are assured and Britain's industrial capacity is moved from weapons of war into peacetime goods. By 1960, Britain is again an industrial power, and while some socialist tendencies are inevitable, Britain's governments fight to find the line between labor interests and those of corporations, and do so with some success. Britain by then is also exporting goods in substantial quantities, including sophisticated goods such as automobiles, ships, aircraft and electronics. This gives Britain the ability sustain its military spending and reduce its debts.
By 1970, plans are underway to replace the oldest of the carriers, with the Queen Elizabeth class of supercarriers. Here, however, as the British retire their oldest such carriers, several of them are sold off. The Queen Elizabeth class of carriers, three in all, enter the fleet in 1974-78. Eagle, Ark Royal and Victorious are sold to Canada, Australia and India, respectively, and all three see many years more service with the Commonwealth navies. British shipbuilding expertise is caught and passed by the Americans, but the close relationship between the two nations is such that British fleet units are often used in the place of American ones.
China begins the negotiations to have Hong Kong back in 1984. Britain is less than keen on giving back the entirety of the glittering colony, which is rapidly becoming one of the wealthiest places under the Union Jack, though they are willing to give back the New Territories if the lease cannot be extended. The Tiananmen Square massacre in June 1989 causes worldwide revulsion of the PRC, and China's trade numbers drop through the floor. Britain takes advantage of this, offering to buy the New Territories outright for a considerable sum. Needing cash to continue covering their needed grain and fuel imports, China takes the offer in September 1990.
By 2000, the Great Britain has 77 million citizens, a $3.2 Trillion economy, and the world's third-largest military force in terms of spending, though Britain's military spending is a high but manageable 3.4% of GDP. A fourth fleet carrier is ordered in 1982 and commissions in 1988. Those carriers - Queen Elizabeth, Duke of Edinburgh, Prince of Wales and Invincible - are the backbone of the Royal Navy fleet. The RN's nuclear deterrent is in the form of four Victorious-class missile submarines, and the RN also maintains five amphibious assault vessels, as well as plenty of support ships. Battleship Vanguard, its usage proven by actions in Suez in 1956 and again in East Africa in 1964, is decommissioned in March 1966 but is kept in such a condition that it can be called back if needed, and as part of this was fitted with CIWS systems and Sea Dart and Exocet missile systems in the early 1980s. It has been called back once, that being for the 1991 Gulf War. Overall, the fleet numbers 112 vessels, not including patrol ships.
This in itself, however is not enough to ensure a British presence - but in combination with the Royal Air Force, which in the 1960s and 1970s built itself a fleet of Avro Vulcan B.3 strike bombers and VC-10 tankers to support them, is enough. These operate from bases in Israel, Cyprus, Qatar, Sri Lanka, Australia, Singapore, South Africa (though the South African bombers were based at Gweru in Zimbabwe from 1981-1995) and the Falkland Islands, as well as in Britain itself.