The simple answer to this question is that there is no clear cut answer. The UK and the USA went from periods of cooperation to hating each other's guts on semi-regular basis. It wasn't until the 1940s that relations normalized in a consistent manner which has, today, transformed into the myth of the unbreakable, historic Anglo-American friendship. However, by and large, this is an invention of the World War II and Cold War era to galvanize unity and cooperation amongst allied nations.

The 1910s and 1920s are an especially interesting case, when you consider that the US, while not a member of the Allies, had been a co-belligerent with the UK during the first world war. Despite this tensions were rather high and the possibility of war was far from far fetched. To quote Churchill himself:

“[While it is] quite right in the interest of peace to go on talking about war with the United States being “unthinkable”, everyone knows that this is not true.”

Austen Chambelain, Wilson, and many others including many members of the general staff of the US/British Army and Navy thought along similar lines. A few more quotes for context:

Wilson (1920):

It is evident to me that we are on the eve of a commercial war of the severest sort, and I am afraid that Great Britain will prove capable of as great commercial savagery as Germany has displayed for so many years in her competitive methods.

Naval Staff Memorandum to Wilson (1919):

Every commercial rival of the British Empire has eventually found itself at war with Great Britain – and has been defeated. . . . We are setting out to be the greatest commercial rival of Great Britain on the sea.

RN Vice Admiral Sir Osmond Brock:

The late war has removed Germany as a possible enemy, but the other effect of the war has been that the United States has become our rival for the carrying trade of the world . . . The United States are endeavoring, as we know, to build up a very large mercantile marine, and they therefore to a certain extent do threaten our existence. Since Great Britain has been a naval power, I think I am right in saying that the ultimate cause of all our wars – even though these causes may apparently be covered by dynastic or territorial reasons, or balance of power – has been commercial rivalry. In the Dutch wars, the Spanish, the French, and the last War, certainly, the ultimate cause was commercial rivalry, and if the United States perseveres in her aims we shall inevitably, not necessarily go to war with her, but we shall come into conflict with her in various parts of the world. The Question therefore arises whether we ought to reconsider the decision of the Committee of Imperial Defence that we cannot fight the United States. I am quite ready to allow that a war with the United States is very improbable, but that it is impossible, I cannot allow.

Planning Section of the US Naval Forces in Europe (1918):

Four Great Powers have arisen in the world to compete with Great Britain for commercial supremacy on the seas – Spain, Holland, France, Germany. Each one in the succession has been defeated by Britain and her fugitive allies. A fifth commercial power, the greatest one yet is, is now arising to compete for at least commercial equality with Britain. Already the signs of jealousy are visible. Historical precedent warns us to watch closely the moves we make or permit to be made!

There are, of course, many, many more similar comments from the era by all sorts of respectable military and political minds. To paraphrase what a history professor in college had once told me about the research of his thesis advisor in high school had done research into this era: "Going off of the diplomatic correspondence between the British and the American diplomatic services, it seemed like World War II was going to break out in the 1920s, and that it would be fought between the British and the Americans."

During the late 1910s (even while they fought together in WWI) the US and the UK were in an arms race that would last into the 1920s. So serious was this arms race and the risk of war that the first real arms limitation treaty, the Washington Naval Conference, was created, in large part, to stop the arms race and cool tensions between the two nations...which it did, somewhat, but you still had whispers of war and military planning on both sides well into the 1930s. Also, of note, one of the major diplomatic achievements of the WNC was the severing of the decades old Anglo-Japanese Alliance (which really irked the Japanese), because the US feared that Britain would co-opt Japan into a war against the US and force it to fight on both the Pacific and the Atlantic.

What really caused the collapse of the Anglo-American rivalry/strife was World War II. And shortly afterwards, the rise of the Soviet Union to superpower status, which then kicked off the Cold War almost immediately after the end of WWII. The combination of having a, perceived, mutual existential threat and the fall of the UK from a position of superpower status effectively ended the rivalry as Britain more-or-less accepted American hegemony and became part of America's SoI.

Hm, never really thought of it in this manner, though it makes sense considering the French funded the colonials.