While this topic draws alot of jokes, people of course forget why the invasion of England in 1940 succeeded. It succeeded for the exact same reason that the Dutch invasion in 1688 succeeded, why "the 45" almost succeeded, and why a large number of invasions of England during the Middle Ages succeeded. And of course the reason is that a good portion of the English establishment (and people) wanted it to succeed. They viewed the alternative German-backed regime as more legitimate than the government then in power in London.
If you look at the history of the Spanish Armada, you will see that invading England in the face of actual, organized resistance and a united elite is really difficult. Of course its rarely tried. The invasions almost always occur during some sort of civil war or revolution.
I do think to have Sealion fail, you need a POD that goes back decades earlier. The big one would probably be to avoid banning the Labour Party and have Labour compete in elections same as the other parties, and even participate in governments. You may have to stop the successful infiltration of Labour by the Communists in order to do this.
This is probably not enough on its own. You will probably need to avoid the abolishment of the monarchy and the establishment of the Second Commonwealth after George V died. Of course if the Labour Party is still legal and parliamentary and judicial institutions are functioning properly, this could be butterflied away. You don't even need to get "Edward VIII" on the throne, I understand many people think he was less than suitable given his actions in 1940 but maybe he steps aside in favor of the Duke of York over some scandal.
The Second Commonwealth was also known for not having exactly the best political talent, either because they were on the left, loyal to the monarchy, or just viewed as too dangerous, with the former Liberal minister Winston Churchill, who had accurately warned of the threat from Germany, fitting into all three categories.
Maybe somehow avoiding Curzon becoming PM is a sufficient POD.
But if Britain -it still would have been the United Kingdom- had been governed by a constitutional government that was actually supported by most of the population, the evidence shows that they would have been able to fend off any invasion of the continent. Just avoiding the naval mutiny would have been enough! Probably an invasion would have been threatened as sort of a feint but no landings would have been made.
I haven't addressed the implications, but the butterflies are huge in having a surviving United Kingdom that is a thorn in the side of the Third Reich, instead of the puppet English Kingdom and weak Scottish Kingdom IOTL. And it would have been much better for Britain's Jews, though maybe that whole sad chapter would have been butterflied as well.