The Stuka was relatively slow and quickly became a favorite target for RAF pilots. Also, the Luftwaffe had fielded less than 350 of them when our hypothetical Sea Lion would have taken place so the ability of the Stukas to inflict that grave a toll on the RN is debatable.
Let us consider what an unsuccessful Sea Lion would have to involve...
Losses of manpower may actually be somewhat even, as the Home Guard will almost surely take losses at a rate above regular forces on either side, with the surrender of German forces on the last day or two serving to even the score. Say, 100,000 lost on each side including POWs(virtually all German).
Naval losses...I've never been a big believer in this image of the battleships of the RN storming into the English Channel and saving the day, based on the overwhelming advantage the RN had without committing these ships. I would go with 20 percent of RN cruisers and 10 percent of destroyers sunk or damaged, with the Kreigsmarine's light craft up to destroyers exterminated.
I might also kill a single German light cruiser and either the heavy cruiser Hipper or a pocket battleship, perhaps on some ill-advised diversionary mission but...no losses among the big guys.
Merchant marine losses, by which read German losses. Doubly important, as all of this ships were important but the barges were utterly vital to German industry. Replacements will be build and new men brought in but I would consider a reduction of German military production by thirty percent for the rest of 1940 to be reasonable. More importantly, there is now utterly no chance of a second German invasion for at least a year or longer.
A point to be made: If the Luftwaffe actually takes control of the air then the likelihood of a British surrender rises dramatically. Ergo, if we assume a failed Sea Lion which collapsed in less than a week, the RAF won the battle. The Luftwaffe can field @3100 fighters, bombers, and dive bombers while the RAF has @750 fighters(plus reserves) and @700 bombers of all types including Coastal Command. What kind of losses should we assume on each side given the assumed early defeat of the invasion?
In a war game of the hypothetical invasion, the RAF had a loss of 50% among fighters(and all reserves), the Stukas suffered 30% losses the first day and were pulled out while the rest of the Luftwaffe suffered over 60% losses.
When you consider that a RAF pilot shot down can get a new plane while a Luftwaffe pilot shot down is off to a POW camp this could be bad for the Luftwaffe entering 1941.
Additionally, if the Luftwaffe deploys the paratroops, note that they would be deployed and resupplied by pilots who were the most experienced men that the Luftwaffe had, the instructors! A heavy loss rate here could reduce the Luftwaffe's training/replacement capacity for several months to come.
Lastly, having punctured the legend of Wehrmacht invincibility, would the British be able to follow with further victories? Given that the British Isles were held by 30 infantry divisions and 5 armored divisions in January 1941, given that the need in North Africa and Greece was real, and given that a German invasion is now impossible, I would submit that perhaps 20% of these forces get sent to Egypt and Greece. At worst, Crete holds and Libya falls, Germany's costs in Greece rise and now must deploy more units to guard the Balkans and Italy.
