Although several British scientists worked on the Manhattan Project during WWII, after the war the U.S. government ended cooperation on nuclear weapons development.

In 1947, in response to concerns about American isolationism and Britain losing its great power status, the British cabinet decided, to resume efforts to build nuclear weapons. 

In October 1952, Britain successfully detonated a plutonium implosion device to become the world’s third nuclear power after the United States and Soviet Union.

Source: Wikipedia