By Jingo If We Do

[Saphroneth]

Here's something which I think might be interesting - a British-Russian war in the 1870s after the Russians decide to take Constantinople.

The primary question here is what the rough balance of forces would be - could the British deploy sufficient force to make a difference? This would be a much more serious test of the Cardwell system than any that happened OTL, after all.
Navally it seems to be a question of British RML turret battleships against Russian ironclads (including the Novgorods, the infamous round coast defence ships).

 

[Escape Zeppelin]

I'm not sure Russia would be able to take the city even without British intervention, but yes British intervention would almost make it impossible. The difficulty is that neither the British nor French want Russia gaining control of the Bosporus and any attempt by Russia to take Constantinople will result in a second Crimean War. The Ottomans are the sick man of Europe but they're far from dead.

If Russia ever thought they could have taken Constantinople, they would have done it.

 

[Just a Rube]

Obvious question is what the rest of the Three Emperor's League does. While the UK+Turkey vs. Russia is probably a loss for Russia (the war against Turkey was enough of a near-run as it was), Austria-Hungary and Germany are enough to tilt the scales the other way (even if France was willing or able to join in).