On the website of the Churchill Centre, which promotes Churchill's principles, he is described as "having made so many deposits in the bank of Religion" as a youth, that he had been "confidently withdrawing from it ever since, never bothering to check the balance--there might indeed be an overdraft."
In the same article, he is referenced as writing that he was a "optimistic agnostic." and "not a pillar of the Church but more of a flying buttress--I support it from the outside."
This presumably qualifies him for either the agnostic or ambiguous categories.