In his diary C.P. Scott, one time editor of the Manchester Guardian records an anecdote which Sir Frank Lascelles (British ambassador in Berlin from 1895-1908) told him about Churchill.
It was when Andrew Bonar Law had become leader of the Conservative Party in November 1911. Churchill was sitting on a settee in the billiard room of a club, Lascelles thought it was a Conservative club. He said to a friend sitting besides him. "Every politician makes one great mistake in his life. I made mine when I left the Tory party. If I hadn't I should now be its leader". "That may be so", his friend replied, "but you can't change sides twice". Churchill leapt up as if he had been shot and shouted "not change twice!" in violent protest."
If Churchill had stayed in the Conservative Party and had become its leader when Balfour resigned in November 1911, and assuming that Asquith still formed a coalition with the Conservatives and Labour in May 1915, Churchill would have been appointed to the coalition cabinet, probably as First Lord of the Admiralty or Colonial Secretary. How would his not being in the cabinet before May 1915 affect the Dardenelles expedition? Would it still have happened?
Presumably Lloyd George becomes Prime Minister in December 1916 as in OTL and Churchill is appointed to his war cabinet, in which he stays after the Armistice and the subsequent 'coupon' general election which the coalition wins by a landslide as in OTL.
If the Chanak crisis of October 1922 had happened as in OTL, would Churchill have supported or opposed Lloyd George? Would he have supported or opposed the Tories who wanted to leave the coalition?
Scenario 1. Churchill throws his support behind the anti-coalitionists, and the Conservatives win the general election with a working majority in November 1922 as they did in OTL, and he becomes Prime Minister. He would not have called a general election on the issue of tariffs like Baldwin did in OTL in December 1923, so there would be no Labour government in January 1924. Also he would not have appointed Edward Wood (later Lord Irwin, later Vicount Halifax) as Viceroy of India with all the consequences for India.
Most likely there would be a general election sometime between the autumn of 1926 and the summer of 1927. Assuming that the Asquith/Lloyd George Liberal split happened as in OTL, probably by 1927 the Liberal Party would have been reunited. There would not have the general election of October 1924 in which they were decimated and reduced to only 40 MPs. The Labour Party would have competed with the Liberals as the main opposition to the Conservatives.
So a 1926/1927 general election could result in a hung Parliament with either the Tories or Labour as the largest party, but with Labour and the Liberals combined having an overall majority. So Labour forms a government with Liberal support and Ramsay MacDonald (most likely he is Labour leader) becomes Prime Minister.
By then Churchill would have been Conservative leader for 15/16 years, so he resigns. He is followed as leader by probably either Stanley Baldwin or Austen Chamberlain.
The Great Depression happens as in OTL. The Conservatives return to power in 1930 or 1931 as part of a National government as in OTL or alone. If such a government in the 1930s has the same foreign policy as the OTL governments then presumably events would unfold basically as in OTL and Churchill becomes Prime Minister in May 1940.
But if in a 1930/1931 general election Labour, while losing, does less badly than in the 1931 general election in OTL. Therefore George Lansbury does not become leader. Perhaps Arthur Greenwood is elected to the leadership.
Scenario 2. Churchill decides to continue supporting the coalition and resigns as Conservative leader when the majority of Tory MPs vote to leave the coalition with probably either Baldwin or Bonar Law as their leader. The Conservatives win the general election in November 1922 as in OTL. Events from then would differ from OTL to a greater or lesser degree.
One possibility is that Churchill and Lloyd George, together with other coalionist Conservatives and Liberals form a Centre Party. If they did that could make a major difference to British politics, depending on how much support such a party attracted.