British neutrality (and the attendant neutrality of Britain's dominions and Britain's ally Japan) abolishes Entente naval supremacy and puts the Imperial German Navy as master of the seas, and dramatically lowers the Entente's strategic reach. The Ottomans don't have to worry about attacks from Egypt and Kuwait, the British Expeditionary Force isn't present to slow down German advances in France, without naval supremacy Russia falls under a harsh blockade...my money isn't on the Entente. I also doubt Italy would intervene on the Entente's side and the United States almost certainly would not. British neutrality is a road to a swift Entente victory.
If Britain stays neutral, I doubt the Ottomans get involved. The British provoked the Ottomans into the war, not so much because they wanted to fight the Ottomans, but because they had so little respect for them that they didn't bother to worry about whether the Ottomans would be provoked by their actions.
