the spy ring happens to be of British origin in the first place , but you didn't hear it from me . ı have heard the Soviet nuclear "threat" would have been credible in the mid 50s , with a minimum number of bombs and planes to carry them to a militarily meaningful range but the 1949 test showed the time table was behind the reality .
That is to say, the Soviet spys - Klaus Fuchs, etc. - were part of the British contingent to the Manhattan Project.
In any case, once Pandora's box is openned, there's no closing it. A big arguement in the 30's was that the Uranium Bomb was "impossible" to achieve; too technologically challenging (the separation problem), too expensive (during the Depression), too futuristic (SciFi stuff - H.G. Wells, Olaf Stapledon); it would never work. But once the Americans fired-off two or three, these arguments were shown to be demonstrably false.
During the Cold War, The Soviet Union became masters of reverse engineering - based often on what data the KGB could provide. Without the spys, the USSR was still a technologically savy country with some of the world's finest physicists and mathematicians, and would have only been delayed a few years (IMHO).