After looking into this more closely, it would seem that the next best choice would be Anthony Eden. Eden and Churchill both led factions within Chamberlain's party. Eden also gained stature after he resigned when Chamberlain followed through with his appeasement policy with Italy. Unfortunately for Eden, after he resigned, he was not as publicly vocal as Churchill. Eden acted more like a refined aristocrat who was watchful of what he would say while Churchill had the gift for gab. The two were rivals and hardly got along while Chamberlain was in power but they shared the same views and principles.
So, from what I was told by the helpful folks during my visit to the British Council at Ortigas Center, it would seem that it is possible that Eden could have been PM if for some reason or another, Churchill suddenly was not available to take over from Chamberlain. To be fair to Churchill, once Churchill took over, he took in Eden and the two became confidants.

To be frank, the guys at the British Council did laugh when I asked about this because they never considered such a possibility. Fortunately, they were intrigued by the idea that they went into a discussion of British WWII politics, to which I was a rapt listener.