Were there tensions between the locals and the empire (like before the American Revolutionary War) or was it purely an economical decision? It doesn't make much sense to me, why would an empire give up so much land inhabited mainly by people so culturally close to Britain? How serious was the idea of an "imperial federation"? Why didn't Britain try to keep at least a few of those big islands, some even uninhabited of Canada? I am very interested in where can I get more information about these issues.
The move to federate these collections of colonies began much earlier, in the 1840s, and stemmed from a desire to establish 'responsible self-rule' within these departments, so that the global empire did not have to be entirely administered from Westminster. By consolidating these far-flung colonies which were all administered distinctly into three stable self-maintaining entities, the British empire was effectively able to streamline its operating procedures. Westminster still controlled Trade, Defence and Foreign Policy at this point, which were the only global issues it really needed to concern itself with.
I'm moving into the realms of speculation, but after WW1 the Ottoman, Austro-Hungarian, German and Russian Empire were dissolved, and there was a general trend towards the self determination of peoples. With such a close union between all four states there would have been relatively little to gain from maintaining the administrative network (especially given the economic strain on Britain at the time), and relatively few consequences in granting the former colonies full self-determination- trade and alliance would still be essentially assured.
Also, it saved them money. Allowing the colonies to run themselves internally meant that fewer British administrators needed to be paid to do things. After WWI, most economies were hurting, so this helped. But the push for self-determination also matters, certainly. It is difficult to justify treating all these territories that just sent men to fight and die for you as less-than-countries when you are promoting the rights of your former enemies to have their own country and run it themselves (a position British took towards newly-formed Czechoslovakia and Yugoslavia).
Canadian confederation (1867) was at least partially a direct result of the American Civil war as well. The provinces had never acted together, each was an independent colony answerable to Westminster directly. But for better self-defense, they were confederated into the dominion of Canada. It was really partly to make Canadians more responsible for their own cost of defense from the American threat, and to avoid the possibility of the US hiving off provinces one-by-one in a divide and assimilate strategy.