If the RAF lost, they would fight on the beaches, they would fight on the landing grounds, they would fight in the fields and in the streets, they would fight in the hills, they would never surrender. And even if their island or a large part of it was subjugated and starving, then their empire beyond the seas, armed and guarded by the British Fleet, would carry on the struggle until, in God's good time, the New World, with all its power and might, steps forth to the rescue and liberation of the old.
So basically Germany would've taken longer to defeat, but total US victory would still be inevitable.