Was there an Anglo-American cold war between the world wars?
Short answerNo. Mutual war plans mainly represented sensible worst-case preparation by the world's two strongest navies, not an expectation of actual conflict.
NotesEach navy had to test itself against the strongest plausible opponent, which naturally meant the other major English-speaking fleet. Planning and exercises built around that opponent exposed weaknesses that a weaker scenario would hide. Modern exercises likewise use friendly states as a capable red force without implying an intention to fight them. Political and technological competition existed, but there is little evidence that the two navies treated a real war as likely.