While Kemal and his associates might have "antipathy" towards the British, the Russians are right next door and want and have wanted control of Constantinople/Istanbul and the Straits forever. Having good relations with a large neighbor who covets what you have, even if they are distasteful (communists) is smart policy. Giving said neighbor an excuse to roll over you and take what they covet is bad policy. Had the USSR collapsed and an armistice in the works in the west, Turkey might have decided to bite off a part of the Caucasus, then again maybe not.