For any seaborne invasion of Britain, the Germans required air superiority (else the RAF could attack the invasion force at sea). However the Battle of Britain was won by the RAF making this impossible.

As to whether or not operation sealion would have worked in spite of this, The Royal Military Academy Sandhurst conducted a 'wargame' in 1974 to answer this question and concluded that such an invasion would have been a resounding failure.

Summary of the exercise: http://mr-home.staff.shef.ac.uk/hobbies/seelowe.txt

I know this answer is not quite the level that would be desired, sorry about that I dont have the sources on me.