First, the Royal Air Force was not at all destroyed. Through 1940 the Germans usually had a small advantage in total airframes, but it was in the neighborhood of a 20% advantage at any given time. Flying defenseless troop transports into an area where your opponent could throw up hundreds of fighters is generally not a terribly good idea. There is no guarantee that the troops would reach the ground... at least not in a controlled fashion.

Second, in 1940 Germany had exactly one airborne division, the 7. Flieger-Division. This accounted for around 22,000 men at full strength. After the battles in Norway and the Low Countries it wasn't yet quite back to full strength. Against this single airborne division the UK had around 24 divisions in various stages of build up and preparation, along with another 11 independent brigades (worth about another 4 divisions). These divisions and brigades also included far heavier artillery and tanks that the airborne divisions weren't equipped to deal with. Now these 28 divisions weren't enough to attack the 150+ divisions that Germany used to conquer France. It was more than enough to repel any airborne assaults.

So an airborne assault would be decimated by air defenses on the way in. Once on the ground, the remaining troops would be outnumbered roughly 30 to 1, and the troops they faced would be far better equipped. If they survived long enough, they'd also run out of supplies in 3-4 days. It's a complete non-starter as an idea.

There are several major problems with this hypothetical airlanding in southern England.

Firstly, the Luftwaffe success in the Low Countries and France in 1940 was far from easy. The Germans managed to win air superiority for Fall Gelb only after a hard-fought campaign that managed to overrun a number of French airbases. Like the rest of the French military establishment, the Armée de l'air assumed that the war would be somewhat protracted, so it planned a national dispersion scheme of its air assets. This meant the Germans practically blundered into destroying the French ability to counter Gelb in the air. French aircraft had to travel to the combat zone while Luftwaffe aircraft had the benefit of operating proximate to their bases in Germany. There were other problems with the Armée de l'air in 1940 such as doctrine and equipment that all contributed to its defeat. Yet, even this victory was dear-bought by the Germans, which lost a quarter of its frontline strength from all causes. These losses were nothing though compared to the Battle of Britain in which German efforts to win air superiority over the British isles came to naught. The Luftwaffe tried to destroy the RAF in the late summer of 1940 and although it was a hard-fought campaign, the Germans could not destroy Fighter Command.

The fact that the RAF was a viable and present force in the field in 1940 meant a massive airlanding was not a militarily viable option to invade the UK. Subsequent experience with airdrops in Crete in 1941, Normandy and the Low Countries in 1944, and the Rhine crossings in 1945 showed that transport aircraft were vulnerable. Not only were they loaded with heavy cargo of troops and their equipment, the transport aircraft were slow and flew in a straight path at relatively low level. In short, they were a massive target. There were large losses of transport aircraft even in conditions of near-absolute air superiority such as Overlord, Market-Garden, and Varsity. The latter successful operation crossing the Rhine saw the Army Air Force lose as many men in the air as the 17th Airborne Division did on the ground. Granted the numbers of the UK's antiaircraft gun defenses were not at the levels of the late-war German Flak arm, but it was large enough to extract significant losses as too was the intact Fighter Command.

This is also a very academic exercise since there was no massive German Fallschirmjäger arm available to invade the UK. The Germans had used paratrooper and glider troops in the Low Countries on a massive scale. Some of these attacks were successful like the Eben Emael raid, but others less so such as the seizure of Dutch airfields. The high profile successes led to the expansion of the two airborne divisions of thr Fallschirmjäger and Heer into properly-sized divisions. This was an expansion that only bore fruit in 1941, in time for the German paratroops to be massacred in the Pyrrhic victory at Crete. Additionally, the Germans in 1940 lacked not only the warm bodies for a UK air assault, biut also the transport aircraft for such an operation. Among the losses in Gelb were a number of Ju-52 transports. The Low Countries had also exposed the deficiencies of German glider aircraft like the DFS 230 which were too small for operations other than small-scale assaults. The DFS 230's replacement, the Gotha Go 242 would be available in 1941/42 as was the heavy-lift glider initially meant for a UK invasion, the Me 321.

So even had the Luftwaffe had managed to wrest air superiority over southern England in 1940, it had no means to reliably convey enough troops in the numbers necessary to subdue the UK. Neither and air assault nor an amphibious invasion were practical when the Germans had no means to conduct either.

In short, they didn't decimate the RAF and thus it was impossible for the German Army to be paradropped upon British soil without devastating losses that would cripple them when they arrived on the ground.

Once these troops, who did make it past the RAF and Anti-Air Defences had organised enough to mount an assault and gain any territory of any strategic value, they would be further crippled by the counter attack from the British Army.

For any land invasion to be successful the Luftwaffe would have had to completely decimate the RAF, sparing enough numbers to be able to destroy the royal navy to allow supplies, mechanized vehicles and more troops to mount a real assault of some degree upon the British Isles.

Unfortunately from a German point of view, that didn't happen. Fortunately from my point of view, as a British person, this was stopped at the first hurdle.

I think you need to understand the nature and doctrine of use of Airborne Troops. Others have explained very well already the need for a significant force and the fact that the RAF was not wiped out.

That said, even if the RAF had been completely destroyed and even without AA defenses what you need to keep in mind is that Airborne Troops are Light Infantry, meaning they can only carry light equipment and limited supplies with almost no artillery, no anti tank weapons (remember this is 1940, no anti-tank rockets, no PIAT, no fancy modern TOWs).

So you drop thousands of soldiers in a very very very disperse landing zone. The comms and difficulties to regroup are considerable and you are very vulnerable as the enemy land forces can attack you in detail. Even if you manage to group and mount an attack you will run out of ammo soon, all your artillery support at that time may come from few light mortars and may be few 37 mm max. How do you resupply? How do you care for the wounded? No field hospital there no ambulances just basic medic attention. You are doomed to be overrun by the locals without external intervention.

These are only few examples but I have barely started with the issues. Hence paratroopers tend to be used for very specific and typically small local targets behind enemy lines until they can link up with the main army force advancing. Most airborne operations in WW2 were very costly, for both sides Germans and Allies alike, from Eben Emael to Crete to D-Day and Market Garden. There is ample bibliography on all of them to read.

If you want to see how messy and airborne operation can go I may suggest you do reading on the less known Vyazma airborne operation where Soviets landed forces behind the German rear in early 1942 around Smolensk.

Edited for typos and structure.