When we look into the reality on the ground circa the time period when Operation Sea Lion was supposed to happen, we see that if attempted the invasion, Germany would have lost a noticeable portion of its force over a rather costly, but not too costly invasion operation.
They would have taken over Britain without too much difficulty, since BEF was crippled and they left their heavy equipment at Dunkirk, and there wasn’t much troop presence in British Isles. Britain was enrolling ‘part time’ soldiers and making up improvised armored cars to make up for the loss at Dunkirk.
Scotland, if they couldn’t take over through any other easy means, would have given them a lot of trouble in the highlands, but wouldn’t be too unlike mountainous parts of Balkans.
So they would have taken over Britain rather acceptably without crippling losses.
Britain did not have much resources like the scarce and valued oil Germany was needing, it didn’t have other heavy industry resources that was not found in Europe.
And after the invasion of British Isles, Royal Navy which would not be totally destroyed in the invasion would still be out in the oceans, and whatever asset Britain had left in other parts of the world would still be there.
Even if Royal Navy was totally crippled during the invasion, Germany still did not have enough naval presence to do anything elsewhere in the world. Leave aside the surface fleet to safely go here and there, but also the logistic capability to ferry anything anywhere -personnel, equipment, supplies.
And such an invasion would totally expose Germany to USSR – while a decent number of troops, aircraft and supplies would be tied up in the invasion of Britain, Germany’s eastern flank would be vulnerable.
And with the build up USSR was effecting, Red Army would have an advantage over entire German army in numbers and supplies, leave aside what would Germany had left in the eastern front during invasion of Britain.
It would be insane for USSR not to attack Germany at that point, since both parties knew that a war in between two differing ideologies were totally inevitable. Not to mention Germans’ “untermensch slavs” psychopathy.
Lets say for a second that Germany did the invasion, and USSR did not attack.
Germany trying to build up a navy to deal with what’s left of Britain overseas, building up a navy for ~5-10 years, redirecting valuable production to shipyards? Could happen if they consolidated their european occupation and marshaled some economy to do it, but by that time the ‘remnants’ of Britain in overseas British colonies would have built up to a considerable problem with US help. That is unless Japanese did not succeed in overrunning Australia and India, which was totally unlikely with US presence.
By that time USSR would have built up o a juggernaut which would easily roll over entire Europe.
So, as you see, invasion of Britain was strategically unproductive and dangerous. Hence the Germany’s turning away from the invasion to deal with Britain at a later date. Which would never happen due to USSR.