Without US involvement, the UK may have suffered a short-lived defeat at Germany's hands, but it would have prevailed in the end. German occupation of Britain would have consumed enough German troops and other resources to have greatly increased vulnerability on other fronts.

I can imagine a German general saying to Hitler, "The good news is that we've finally defeated those pesky British. The bad news is that we're going to have to send 25% of our entire army over there to keep them defeated."