But I found this where Churchill references the heroic efforts of the RAF who turned back the Luftwaffe in the Battle of Britain.

"Never in the field of human conflict was so much owed by so many to so few"

Militarybook may be the one most qualified to answer this question. But I believe the simple answer is that the RAF did stop Hitler from mounting an amphibious assault on Britain. After the Battle of Britain, Hitler decided that he needed his remaining bomber units to launch the invasion of Russia.

So in the short term fatwollit is correct. The RAF prevented the invasion of Britain without the direct help of the US military. Longer term, we can only conjecture.