Imperial federation, membership and a four-superpower Cold War

How would the world differ if the British Empire became an imperial federation instead of the Commonwealth?

The counterfactual depends on membership, cohesion and formation date. Retaining India or the Gulf states would produce a different federation from one without them.

Clarke's counterfactual envisages a closely integrated imperial federation producing a four-superpower Cold War. Its strength depends on when federation happens and whether India remains a member. Kenya, Nigeria, Tanzania and South Africa would also change the federation's scale, while retaining the Gulf states would give it a large share of the world's oil supply. The scenario allows the admission of countries that had never belonged to the British Empire, as the Commonwealth later did. The proposed post-Cold-War relationship with the United States is cooperative, with both states retaining substantial power. These are possibilities raised in the discussion, whose detailed consequences are left uncertain.