A surviving British Commonwealth in the Cold War

How might the Cold War change if Britain retained enough economic capacity to preserve a powerful Commonwealth?

The West could become an Anglo-American partnership, with Britain leading around Europe and the Atlantic while the United States led in the Pacific, supported by a Commonwealth trade and defence bloc.

The scenario uses fictional matter-replication technology to remove Britain's postwar shortages of energy, food and industrial inputs. With the empire able to avoid much of its debt, the likely result is a looser Commonwealth rather than direct rule from London. That bloc could combine trade, defence and political coordination, giving the United States an equal partner in an Anglo-American alliance. Britain would take the lead in Europe, the Atlantic and the Mediterranean, while the United States led in the Pacific. A later answer adds that coordinated Commonwealth votes could carry unusual weight at the United Nations. The premise is science fiction, but the reasoning focuses on resources, debt, alliance structure and spheres of responsibility.