The plan for Sealion was unrealistic, unworkable, and unlikely to produce a positive result. However, the big thing making this so wasn't so much the RAF, but the Royal Navy instead.

Any successful amphibious operation requires maritime superiority, if not supremacy. Transports are easy targets, and can be difficult to protect them against even a small force. This was proven over and over again in WW2, from Narvik in 1940, through to Dieppe and the Japanese attempts to resupply Guadalcanal. The Kriegsmarine had no way to win such superiority. They were very heavily outnumbered in terms of surface combatants; the Kriegsmarine had, in total, 10 destroyers. In the Nore Command (covering the South-East and East coasts) alone, the Royal Navy had 32. Looking at larger ships repeats this balance of power. This sheer discrepancy in numbers meant that the Kriegsmarine had no chance to gain superiority alone. This analysis ignores factors like the poor quality of the Kriegsmarine's destroyers, and its commanders.

However, the Kriegsmarine's surface ships were not the only way the Germans could attempt to gain maritime supremacy. Submarines and aircraft were both available, and could be used in an attempt to wrest control of the Channel. Unfortunately for the Germans, neither of these would likely have the effect needed. The U-boat arm was large, with about 40 submarines available in June 1940. These had been effectively used against British merchant shipping, and had scored several major successes against British capital ships. This would suggest that they would be effective in seizing maritime supremacy in the Channel. Against this, though, stand two major points. Firstly, the waters of the Channel are poor waters for submarine operations. They are shallow, with several major sandbanks. These restrict submarine operations, and make them easier targets. The Channel had also been heavily mined to prevent U-boats travelling down it. Secondly, U-boats required long turn-around periods in port. Crew comforts aboard U-boats took a distant second place to the equipment required to fight the sub. This meant that crews required long periods in port to maintain health (both mental and physical) and fighting effectiveness. To use the U-boats in an invasion would mean removing them from operations in the Atlantic a month or more in advance. This would give the British breathing room, allowing them to import more armaments, ammunition and food. It would also allow them to move more destroyers and escorts to the areas where invasion threatened. Clearly, submarines would not work to allow the Germans to invade Britain.

Aircraft could also allow the Germans to gain naval superiority. German and Italian dive-bombers would allow them to successfully land troops on Crete a year later, even in the face of attacks by the British Mediterranean Fleet. In the process, they would cause heavy damage to the Mediterranean Fleet, sinking four cruisers and six destroyers. Land-based aircraft would also prove effective against warships in the Pacific. However, there's little evidence that the Luftwaffe would successfully deter the RN. The exceptional results during the Battle for Crete were a bit of an outlier - the Mediterranean Fleet, operating several days travel from its bases, was low on AA ammunition. This wouldn't be an issue for Home Fleet, which would be operating practically on its doorstep. The Luftwaffe and Regia Aeronautica were also operating in near-complete air supremacy. The Luftwaffe could not gain this over the UK, as Fighter Command could simply withdraw to airfields in Northern England. These airfields could not be hit by escorted bombers, and hence any attack on them would take heavy casualties (as an attack on North-East England on the 15th August 1940 did). Finally, the operations in Crete came after a year of training in anti-shipping attacks. During 1940, the Germans repeatedly attacked British destroyers in the Channel - both those escorting convoys through the waters, and those evacuating troops from France, Holland and Belgium. From the start of May 1940 to the end of October, 11 British destroyers were sunk, and 20 seriously damaged. However, of those sunk, four had been moored or were otherwise not moving. Of those seriously damaged, eight were in harbour, or moored to a buoy. However, roughly 40 attacks against British destroyers, mostly against ships at sea, did little damage to the target. Many more did no damage at all. The majority of air attacks against British ships at sea in 1940 left the ship in a capable condition to further fight. Even if losses to aircraft were higher, there's no evidence that this would cause the RN to give up. All of the ships lost or heavily damaged to air attack were so damaged during daytime attacks - the RN could simply cut its losses by attacking at night. Secondly, things like Operation Pedestal, or the evacuation from Crete, show that the RN was willing to accept major losses to complete goals that are insignificant compared to protection against an invasion. Finally, the Luftwaffe would have several other targets to hit, including airbases, ground troops, coastal defences and transportation links. This would dilute the German anti-shipping efforts, in a way that wasn't present at Crete or Dunkirk. All of this evidence points towards German aviation being incapable of preventing the RN from responding in force to a German invasion.

As I hope I've shown, the Germans had no way to obtain the naval supremacy in the Channel they would need to carry out a successful invasion.

Sources:

The Defence of the United Kingdom, Basil Collier, HMSO, 1957

BR 1886 (C.B. 4273 (52)) H.M. Ships Damaged or Sunk by Enemy Action 3 Sep 1939 - 2 Sep 1945, Admiralty, 1952

Crete: The Battle and the Resistance, Anthony Beevor, John Murray, 2005

Operation Sea Lion - An account of the German preparations and the British counter-measures, Peter Fleming, Pan, 2003