OOC: I don't know how plausible these things are, but I'll try. The TL is not just about the Bomb. Please enjoy.
Part I: The Great European War and the Golden Age of British Physics
Chapter 1: The Physicist Diaspora
19th-20th Centuries
Over the century, leading men in Britain were influence by the more enlightened intellectuals of the era. Many of these intellectuals were scientists, philosophers and persons of thought and method who wanted to spread knowledge in Britain and they convinced the government and wealthy landowners to invest in the existing schools and universities as well as build specialised ones. These schools flourished with the funding and became good attractions for people who wished to further their education. The prestige of these schools and the perceived value of science led to Britain becoming a likeable residence for scientists and researchers. France and other countries in Europe adopted this investment in their universities and the sciences and soon, there were many many prestigious universities in Western Europe, and this part of the continent quickly became the destination for scientists and fledging scientists who wanted to advance in their fields, receive benefits or make a name for themselves.
1927
J. Robert Oppenheimer decides after graduating with a Ph.D. from the University of Göttingen and, instead of returning to the USA, decides to resettle in the United Kingdom. His family tries to convince him to return home but he states that he has found love on the island during his studies in Cambridge. He becomes a naturalised citizen in the 1930s and marries his girlfriend-turned-fiancée sometime in this decade as well.
1933
With the rise of Nazism in Germany, Albert Einstein escapes to Canada. In the United Kingdom of Great Britain and Northern Ireland, more suspicious and military heads prevail and the nation begins its rearmament early, what with the revanchist and militarised policies of the Nazi regime. The UK declares that it is willing to accept any and all distinguished scientist who arrive on its shores, and this is done in the form of small government grants.
1934-36
George Gamow and his wife defect from the Soviet Union and travel to the United Kingdom, after attending the 1933 Solvay Conference. A year later, he manages to convince Edward Teller to accept an invitation to work in Britain. He attempts to try and contact his friends and old co-workers, with varying results. The British government allows MI6 to conduct black operations within Germany in order to abduct German scientists to conscript into any war effort.
The Second Italo-Abyssinian War provoked a mixed response from the governments of the League of Nations. Emperor Haile Selassie gave a stirring speech to the assembly, but his resolution for the world body to deny recognition of the Italian conquest was defeated. In addition, he was not granted a loan to finance a resistance movement. Adolf Hitler had supported the invasion before it had began, and Britain would recognise the conquest in an official agreement with Italy in 1938. Japan recognised it in March of 1936 and in turn, Mussolini recognised the Japanese occupation of Manchuria.
Britain had declared an arms embargo on both Ethiopia and Italy in June in an attempt to broker peace, but France had already signed an agreement with Italy which gave the latter nation parts of French Somaliland (OOC: now Djibouti), redefined the official status of Italians in French-held Tunisia, and essentially gave the Italians a free hand in dealing with Ethiopia. In exchange for this, France hoped for Italian support against German aggression. Since Italy had stated that any act of supplying Ethiopia was an act of unfriendliness towards the Italian Empire, Britain had decided to place an embargo on both nations, although Britain also cleared its warships from the Mediterranean, further allowing Italy unhindered access. The militarised government had wanted Italian friendship in the event of a war with Hitler's Germany.
1937-38
Austria is annexed by the German Third Reich in March and, in September, Adolf Hitler demands that the Sudetenland be 'returned' to Germany. Despite the militarised government of Britain, Neville Chamberlain still pursues a policy of Appeasement and the Munich Agreement cedes the Sudetenland to Germany. This makes many of the people in his government to start to really dislike him.
During the talks with Ireland over many of the Irish grievances of the Anglo-Irish Treaty, which resumed in November 1937, Neville concedes to his government's demands to bring along more adamant and forceful negotiators. In March, an agreement was reached after effective use of the more stubborn of British negotiators and many compromises were made, but most had forced the Irish to accede to the United Kingdom's positions, including the keeping of the Treaty Ports.
Stanislaw Marcin Ulam and Enrico Fermi both emigrate to France in a coincidental choice of similar times. In December 1938, Otto Hahn and Friedrich Wilhelm Strassmann send a manuscript to Naturwissenschaften reporting they had detected the element barium after bombarding uranium with neutrons; simultaneously, they communicated these results to Meitner, who had escaped from Germany to Sweden earlier that year. Meitner, and her nephew Otto Robert Frisch, correctly interpreted these results as being nuclear fission.
In December on 1937, the League of Nations finally condemned Italy's occupation of Ethiopia, which resulted in Mussolini's withdrawal from the organisation. However, Chamberlain decided to follow his predecessor's example and declared support for Italy and contested the resolution (OOC: IOTL, he wanted an Anglo-Italian alliance against Hitler, so I think this happened anyway). The British ambassador had decided to give an impassioned speech declaring his country's support for Italy (although mostly supportive, there was a varying range of agreement in the government as to whether the occupation was lawful or not), but he was decidedly ignored in the resolution. Benito Mussolini sent a letter to the ambassador thanking him and his country for his help.
1939
The Nazi invasion of Czechoslovakia saw an even more elevated increase in military production and a general hatred being formed in the more militarised government against Neville Chamberlain. Winston Churchill, at the forefront of the criticism, tells him "You were given the choice between war and dishonour. You chose dishonour and you will have war."
With Europe teetering on the brink of war, Neville was humiliated that his policy hadn't worked and attempts to rectify the situation. However, his government (and France) signs a treaty with Poland promising them protection from Germany. The treaty is activated following the Invasion of Poland in September and France and Britain declare war on Germany.