There would be no Crimean War
yes Nicholas I of Russia coined the phrase Sick man of Europe with the help of british journalistWas Russia even going to go so far as to try that at this time?
Would the British help the Turks with sending the RN in to the Black Sea to ensure the Russians can't use their navy or water transport to assist in their campaigns against the Ottomans. Some small land components, perhaps artillery etc. The sort of land component you saw OTL, no way. Absent the French land component, an invasion of the Crimea with only British troops simply is not feasible - they would be tremendously outnumbered. Using Ottoman troops against the Russians in Crimea is probably militarily impractical and would be politically unwise.
So...no "Crimean" War
The Russian invasion of the Balkans stalled before French and British troops even arrived. Russia isn't going to have much success in an alternate Crimean War without French involvement, the Ottomans did a fine job repelling them on their own and Russia probably couldn't hope for more than taking another slice of the Romanian principalities as long as Austria remained hostile to their movements in the Balkans. Even in OTL the Crimean campaign was in large part a political show by Britain and France to justify their entry into the war.do you think Russia will take Constantinople or do you think Russia just take some more land from Ottomans
I would think that a serious British force augmenting the Turks in the Danube could be beyond their capabilities.