Captain Ed,
As regards the panzers stopping, perhaps there was an element of Hitler letting the British escape with some sort of "dignity", thinking some sort of peace could still be negotiated.It COULD have happened, as there were appeasers such as Lord Halifax and Chamberlain around- but one man in particular stood in the way- WSL Churchill.
This may appear strange, but there is evidence that Hitler believed there was a place for a British Empire which could accommodate Germany.Main preoccupation was primarily Russia.
As regards the R.N., believe the whole situation was so fluid and happened so quickly(it was blitzkreig remember-lightning war)the Home Fleet simply had no time.
I'll tell you where the navy was a month later though-Tels-El-Kebir, where it blew up the French fleet after it was given, and refused several options (Churchill considered it was a threat and may have come under German control).
Hope this helps.
Finally may I state categorically there is no question of lack of respect for ALL of the dead of the tradgedy that was WW2- not just Britain and France, but bigger losers such the then Soviet Union.
To suggest otherwise I consider an insult.