Airborne assault of London area, which I see you're suggesting (that's where Churchill and the King would be), is a wild fantasy

If you're trying to say that losing BEF would mean Britain had no troops to defend itself from a bunch of paratroopers, then consider that BEF numbered around 400k, while the whole British army in the summer of 1940 numbered around 1.5 mln. Moreover there was another 1.5 mln strong volunteer Home Guard armed by the end of June 1940.
To your remark of German paratroopers eating newbies for breakfast - no paratroopers eat any enemy for breakfast just after drop. They're dispersed, disorganized and need time to get together. There's a reason why they're usually dropped BEHIND enemy lines in zones judged as SAFE, where there isn't much enemy activity and not much opposition is expected. Paratroopers usually are elite units and can be very formidable opponents, but in defense or attacking isolated and surprised enemy, not heavily defended capital city of a major European power. IT'S NOT AN ACCIDENT that airborne assaults of dense urban areas haven't been tried by ANYONE in history of warfare, even though instant attack at the heart of enemy and decapitating its government would definietly be an attractive option for everybody. The greater London area was saturated with AA defenses which would make minced meat of Airborne attackers. The ones who'd make it to the ground would be dispersed in unfavorable urban environment, find it impossible to form any cohesive unit, and under instant attack. At the end of the day the confused remnants would probably get arrested by London constabulary force