Sealion is kind of...oh, what's the term for it. I can't recall...at any rate, it was never practical. The practical impact of the attacks on British airfields and strategic targets is significant, but the effect of the change of policy to terror strikes is a bit overstated. The RAF consistently had the benefits of both numbers and the home field (with attendant consequences on those pilots forced to bail out), as well as technological benefits. Depending on your source (Overy, et. al.), pilot numbers were actually growing throughout this period, as were the number of airplanes actually in the air, in spite of strikes against factories and airfields, with the exception of the peak period in September. Even during the worst of this period, when 13 airfields were struck, only two were put out of commission for any length of time (that is, more than a few hours), and precisely one Sector Station was shut down at all (two hours). However, this period ended not just with the change in target priorities, but also by the shift to night raids due to the severe losses the Germans were also taking in their daylight attacks. In other words, if Germany had maintained their existing target priorities and daylight raids for maximum efficiency, they would also have very efficiently depleted their own aerial forces.
Also, it's been suggested that they could simply go after the convoys in greater strength. In addition to the range issues brought up by Sergarr, this is actually exactly what was done - German airplanes were used in not only direct bombing, but were even more critical in scouting for targets that could be relayed to German submarines in the area of operations since they could do this without ever coming into range of the escorts themselves, such as the Flowers which were armed solely to face off against both aerial and submarine foes. In fact, the aerial situation became bad enough that the Allies actually developed a handful of specialized Hurricane launch catapults for merchantmen (termed CAM, for Catapult Aircraft Merchantman) to combat this, even though each launch would essentially mean writing off the Hurricane due to a lack of places to land the thing. It's also critical to remember that in many respects, the best naval bombers were also specialized roles for aircraft; you can't just slap a torpedo on the bottom of a Stuka and call it good (though they actually did build a thousand Ju 87R which more or less did precisely that by using drop tanks to boost their range, not to mention the Ju 88 and the He 111J which was aborted due to manpower requirements). The critical issue blocking German naval bombing was their early disinterest in torpedoes (resolved only after 1942; literally, monthly German torpedo production at the start of World War 2 could be counted on one hand), not to mention the significant land-based pressures placed on the Luftwaffe caused by the launch of Operation Barbarossa in the East - Hitler could not allow the Red Army time to recover from the effective devastation of its officer and NCO corps, not if he wanted to fulfill what was the entire purpose of his ambitions in the first place, and detaching the entire Luftwaffe to go haring off after some ancillary foe trapped on their islands would have had significant strategic consequences.
That said, if there was some ASB intervention that resulted in a German conquest of the British Isles, it would have significant practical consequences. Moving the production facilities out of Britain would not have been as practical as the Soviet transfer of industry beyond the Urals due to the lack of railroads or land transportation connecting Canada to the UK, but would not have been completely dire so long as American industry remained beyond German reach. Political continuity would have been maintained, certainly; while the Royal family spoke strongly about never evacuating Britain (most famously, the Queen-consort's statement that "her children would refuse to leave her, she would refuse to leave her husband, and her husband would never leave Britain", if I recall the paraphrased quote properly), I suspect that if the situation reached the point where both London and the Plan Yellow evacuation points fell to invading forces, they would have been put on the first boat to Canada even if Churchill literally had to personally frog-march each one of them on. Moreover, they would very likely successfully evacuate the bulk of the British government proper, including Churchill himself (again, by force if necessary). The major consequences of a fall of the Home Isles would have been the fact that it would have denied the Americans (once they entered the war; I do not believe this would have been altered by a Fall of Britain scenario) a ready staging base just off Festung Europa. American staging would have relied far more heavily on Iceland (the Greenland-Iceland route that became so essential to naval planning during the Cold War, but in World War 2 could not be covered by land-based aircraft until 1943) and the Azores, with Operation Torch securing preponderance; either southern France (Dragoon) or Italy (Husky, etc.) would have become the primary axis for invasion due to their proximity to staging facilities in North Africa, in spite of the unfavourable terrain, or else the liberation of Britain would have become the first priority, with consequences for the advance further on into northern France.