Given that Britain and Russia were on the same side of World War I, it's pretty surprising how lukewarm their relations were during the 19th century, much to London's almost certain regret after the Bolsheviks took over. The British worked to thwart Russia's ambitions in the Balkans where they wanted control over the Bosporous, they had their famous "Great Game" over Afghanistan, and they supported Japan during their war against Russia in 1904, because they didn't want them taking over more of China.
Is there any way Britain could decide to accomodate Russia's ambitions, or were they too scared of this potential rival?
Of course, everything could be written off on "not feeding the bear" considerations but quite a few of the reasons were either a pure paranoia or an idea that only Britain is entitled to do whatever it wants and to expand as far as it wants and that everybody else must cave to its wishes (which was, IIRC, Palmerston's opinion). Obviously, not everyone had been agreeing with that view, hence a lot of the bad feelings related to the British and Russian expansionism in the CA.
However, it does not look like the Russians of that period shared the British animosity: the British "researchers" of the CA had been routinely well-received on the Russian territory. But, with the main purpose of the Russian expansion in the area being opening of the new markets for their goods, the British demagoguery about the free trade in the region was mostly ignored. Was area of the today's "stans" of some critical importance for Britain? I doubt it. Were Russians seriously planning invasion of India? It is not even funny unless geography and situation in Afghanistan are completely ignored. Eventually, it proved to be reasonably easy to establish a mutually-acceptable border.
As far as Far East was involved, I can't quite get the reasons for the British fears: it was on a VERY far end of the Russian logistics and the OTL arrangements with China did not noticeably infringe upon the British interests. British support of Japan served Japanese interests but how did it serve the British interests? Russia did not and would not have a serious naval presence on the Pacific, clearly did not plan any attack on the British colonies there and its trade with China had been mostly overland (aka, Brits could do nothing about it and how about the "free trade"?). When it was too late, Britain tried to limit Japanese naval buildup and within less than 4 decades after the RJW it had its colonies attacked by the same Japanese whom they helped to grew up into a major military power. BTW, I'm not sure if the Japanese activities in China (like rape of Nankin) had been beneficial for the British commerce either.
Britain supported unification of Germany under Prussia (how about not feeding the "Prussian bear"? Berlin, not Moscow or St-Petersburg has it on its coat of arms), and we know his
this ended.
Britain spent a big part of the XIX century preventing disintegration of the Ottoman Empire and then had to spend a considerable effort fighting against it in WWI.
So how about a general wisdom of the British politicians and their ability for the long-term analysis of their actions?