Maybe the war starts over Russia's remilitarization of the Black Sea in the 1870s, in violation of the Treaty of Paris, which the British effectively ignored in OTL.
Wouldn't this be in the Pre-1900 Discussion Board with a POD of after 1860? It just seems fairly obvious unless something is totally amiss or there is indication of softness of the brains.
that leads to Britain demanding an apology, which Russia refuses to give, and Britiain allies with Japan against the Russians. Russia is beaten even more badly in the Russo-Japanese War, maybe Japan gains influence of the Priamurye or it is returned to China, and Russia is alot more weakened in the next decades... and there might still be a Franco-Russian Entente, but neither the Russians nor the Brits are going to want to corporate with each other.