Do the British really consider themselves a third bloc historically? Even soon after the Anglo-Entente War, they were fairly cordial with the other European monarchies which were F.E.K. members, mainly due to having a greater threat in the U.S., which wanted to spread technocratic rule to Canada and Britain's other New World colonies, and even after the détente the I.F. has remained on good terms with the rest of Europe. They may not be a formal member of the F.E.K., but they're clearly aligned towards their fellow monarchies on the mainland.
Well, there's a reason I put in in inverted commas
I see what you're saying, and there are lots of cases where Britain has leaned more towards Europe. The Calais Accords of the 1930s are one great example - the provision of joint patrols between the Royal Navy and the various European fleets in the Atlantic are commonly thought to have been a response to increasing US naval buildup in the Caribbean and on the Great Lakes.
I would hesitate to place them firmly in the European camp, however. It's important to remember that the original rise of the Franco-German partnership was a significant challenge to Britain (partly motivating the Imperial Federation movement, which is why I was asking about its plausibility in a timeline without rapprochement in Europe). The Naval Races of the 1890s and 1910s between Britain and the F-G Entente were a realm threat to Britain's imperial position.
And of course, as HIM Dogson mentioned, the Partition of Belgium in the leadup to the Great European War was the big moment where Britain realised it would have to abandon its commitment to preventing a single, hegemonic bloc forming on the Continent. It was that or making up with the hated Russians, which is vaguely plausible but unlikely, given the nature of the regime.
Now of course these events never forced London into America's arms, and relations between Britain and the continent have improved since the Great Eastern War and the War to End All Wars (dynastic relationships helped there, of course). But I would still hesitate to place the British Commonwealth wholly in the European camp - there are still significant disagreements, particularly over Britain's insistence on upholding the Two-Power Standard in navy size, even if that is a mostly theoretical discussion these days.
India was always a lost cause once decolonization began in earnest; maybe you could get a more unified country instead of the mess we have in the subcontinent today, but even then that's unlikely due to the sheer diversity of the lands of the former British Raj. The British weren't very popular in most of Africa (save, of course, for Cape), so decolonization there was also pretty inevitable.
I quite agree. I think a united India is almost totally implausible - the cultural and religious diversity is a non-started for any type of uniform nationalism. 'India' was a British construct, and the fall of the Raj inevitably left us with that patchwork-quilt of a confederation we see today. It would be interesting to see to what extent a more prolonged British presence there (perhaps into the 1920s, after OTL's Great European War) would produce a wider regional identity.
I'd also agree about Africa. I think the Cape and the Suez Sovereign Base Area is about the maximum they can reasonably keep in continental Africa - and of course the latter exists on the sufferance of the King of Egypt.