Britain will never support any initiative that gives the Russians the Turkish straits. They would immediately try to find allies on the continent. France, the Ottomans, and likely Italy. However, France will not risk war with the Dreikaisertum ever. They know very well that Italy and the Ottomans are dead weight and Britain could at best draw away Russian manpower to Central Asia, but that still leaves France fighting Germany on her own.
This is very true. There's also the tensions between Germany and Austria to consider also, I think Germany would get tired of having to carry that alliance