A large scale invasion of England in mid 1940 was a logistic impossibility. Never mind total air or sea control or the strength of the German army. In an operation sense, it was totally undoable.
The initial calculations made by the German high command were that the invasion of England would require 34 divisions, and it would take 2 1/2 months to get them disembarked, if they were unopposed. German plans called for the complete control of the English Channel for a minimum of 11 days and a clockwork bus schedule of cargo barges that ignored the infamous Channel weather, to get just 9 1/2 infantry divisions and their equipment across in the initial assault phase, including two airborne divisions and 1 1/2 assault divisions landed on the first day.
The Sealion plan was then revised down to 11 divisions as they realised that they had less than a third of the transport assets that they required. It was further revised downwards to 9 divisions as the High Command studied the operation and its requirements in more detail. If Dover and the other ports further south were not usable (due to sabotage) or not captured in the first 4 days, it was concluded that Germany would be only be able to support 4 divisions in the field. Given that the ports were among the first things marked for destruction by British forces in case of invasion, it was unlikely that they would of been captured intact.
Unlike the Allied cross channel effort in 1944, Sealion had no provision for paralysis of communications or transport in the landing area, no initial bombardment by heavy bombers, almost 0 organic artillery support (just 36 converted barges with 37mm guns and a 75mm howitler), no naval artillery support (the German Navy was assumed to be fully busy with a RN that outnumbered it 5 to 1 in surface combatants), no specalised beach assault craft and no specalised training for its troops, apart from the 2 mountain divisions detacehed as 'cliff climbing' troops.
Germany never got more than 2/3 the number of barges, tugs and motor launches that it calculated it needed to launch a cross channel invasion. Army commanders were almost self-delusionall about the difficulty of the crossing, terming it a 'river crossing on a wide front'. Coming off the victories in France and Poland there was a pervasive belief that the German army could simply roll up the British army with ease. However, the plans for Operation Sealion didn't include sufficient logistic support to allow large armoured or artillery formations to operate.
Sealion was a serious possibility only in the early days of May, when there were almost no heavily manned or fixed defensive positions along the southern coast. By August, the British had created a much better defence network on the southern and eastern coastlines. Before that time it may of been possible to land a small raiding force (1-2 parachute and glider divisions and 2-3 infantry divisions) and capture airfields and small ports in southern England intact. Reinforcements could of been brought in, but given the wastage rates of earlier battles, even this small number of divisions would of completely absorbed most of the barge traffic and cargo capacity in Northern Europe .