The idea of Britain allying with the Turks is at least twenty if not thirty years out of date. Sultan Abdul Hamid had clearly shown a preference for Russia over Britain after the occupation of Egypt. By the time of the 1894-96 Armenian massacres, the British were trying to enlist Russian aid in deposing the Sultan
The Russians were much more receptive to Turkish requests for an alliance before the war. Anglo-french resistance to offering Turkey aid against the Balkan states ended the Russian Turkish talks. In the end, the Ottomans went to war as much over grievances with the French and British as with differences with Russia especially the capitulations.
TheSultan was especialy opposed to war
That said, information was rather freely given in the era and knowledge of the straits rather freely known by everyone.
I'm really only basing the post on the word of one submarine commander who successfully penetrated the Straits underwater, and bemoaned the Whitehall Mandarin's decision to unnecessarily put his (and his crew's) neck on the line. How much of his opinion was hearsay, and how much to reliable sources is open to conjecture. The idea that such Intel would be arbitrarily given up is so dissonant to 21st Century thought that I find it interesting.