Stumbled onto this old post but it's quite interesting. I would have to say that such federation would be incredibly difficult to start. Self-interest and nationalism would certainly kick in, and with the lack of non British descended dominions and colonies (which had some of the most valuable resources i.e spices from India) in the federation (hypothetically becoming independent states) the incentive of being in a political union with Britain, is gone to be frank. Political union on a global scale would have been an incredibly difficult procedure, even in today's standards, and independence movements would spring about all over the federation. If Scotland (a closely tied country both geographically and politically) had an independence referendum, then you can be sure member states would have their own. The point being it wouldn't last long even if it was somehow formed. Would not be a long term solution. A trading bloc however with the former colonies and dominions..... Is also very unlikely, but far more plausible than a federation.