That wouldn’t have happened if the US hadn’t entered the war.
Looking at the big picture, atomic weapons seem to only have a few uses.
They were used twice in World War II for strategic bombing. If Britain had gotten atomic weapons prior to VE Day, it very likely would have used them against Germany and they would have caused a German surrender. But Germany surrendered anyway so that wouldn’t have changed the outcome of the war.
Atomic weapons are useful as a threatened strategic defense. If somebody attacks your country, conventionally or with nuclear weapons, you can retaliate with your nuclear weapons. But this doesn’t seem to have been an issue - nobody threatened Britain in the period between 1945 and 1952.
Atomic weapons have a prestige value. They’re considered the biggest weapons in the world so the countries that have them are often regarded as more important than those that don’t. But again, this was a non-issue: Britain was regarded as a major power already before it got its own atomic weapons in 1952.
I’m just not seeing how an earlier nuclear arsenal changes anything of significance for Britain. The United States has eclipsed the United Kingdom for a number of different reasons since 1945. A temporary lead in atomic weapons wasn’t going to change that. And the European empires broke up for a wide array of reasons; nuclear weapons were not (and did not) turn back that tide.
I’m not saying that the colonies were GUARANTEED to get their independence later. It’s certainly a strong possibility, however. Also, please note that I’ve pointed out (a few times) that having the bomb wouldn’t be the only way Britain would be ‘stronger’ if it had won the war without America’s help.
Frankly, it’d be a bit weird if a stronger, more confident Britain that had much bigger weapons than anyone else didn’t end up keeping its colonies for longer. If the colonies were costing too much to keep then they might well have let them go, but unwilling emancipation would be less likely.
Britain shares the technology with Canada. Cries of “Forty-four forty or fight!” echo through the land.
Whether or not Britain could have developed the atomic bomb (and yes, while they did initiate the first real nuclear weapon development program in the Tube Alloys program, later transferred to the American Manhattan Project along with the predominately German, Austrian, and Swedish refugee physicists and chemists who worked on the program), as pointed out by Polycarp, Britain was already hemorrhaging money to maintain the Empire even before the expenses of WWII. This, and various growing independence movements on the Subcontinent and Africa spelled then end of Britain’s globe-spanning influence.
One interesting but entirely hypothetical line of inquiry is what would have happened in Eastern Europe and Central Asia had Britain not been so preoccupied with packing up the bus and getting out of the empire business. Churchill was an early but constant voice about the danger of Soviet expansionism into post-WWII Europe, and his prognostication turned out to be largely correct. Unfortunately, the British public, fed up with over five years of warfare, had no taste for fighting another European land war with an enemy that had a number of strategic and numerical advantages, and the Soviet Union gorged itself at the buffet of Eastern and Central Europe with the tacit approval of the other Allies, much to the dismay of Poles, Czechs, Hungarians, the Balkans, East Germans, and so forth. Ironically, allowing the Soviets to absorb these nations prolonged its existence by decades as it drained them for labor, resources, and manufactured goods that Russia and the Ukraine itself couldn’t produce, as it was failing economically even before the costly involvement in the Great Patriotic War.
Stranger
In the aftermath of the war the soviets took less land than they could have done and showed no inclination towards further expansion, hence their abandonment of the communists being massacred by the newly western-friendly former fascists in Greece and of the Italian Left as it had its electoral position subverted by the CIA.
And the Soviet Union propped up the Eastern European and Cuban economies throughout the post-war period, right up to the time when it became such a burden they gave up.
The reason that the Soviets did not support the communist in Greece is because of the Percentages agreement between Churchill and Stalin. In 1944, Churchill and Stalin divided their spheres of influence in SE Europe. The USSR exert their control over Romania and Bulgaria; the UK would exert control over Greece; both the USSR and UK would equal exert control over Hungary and Yugoslavia. Since Greece was agreed to be in the British sphere, Stalin did not proved support to the communist there because he did not want the UK to encroach on the Soviet control in Romania and Bulgaria.
And where does the total soviet domination of Hungary come into it?
Really the percentages agreement was just to appease churchill, it was never put into effect. There was no provision in it for any state to be occupied and dominated by either side.