Pontius - quite right. Quite a few people call the BoB a draw. Cobblers. The German aim was air superiority. They didn't get it. Ergo they lost.
The point unixman makes is a good one.
The barges in the Channel ports were just that - barges, crudely adapted to carry things they weren't made to (tanks etc).
They were made for canals, not the open sea. Any hint of a swell, waves, chop etc and they would have floundered without any help from the RN (who would have inflicted heavy damage anyway).
Also, look at the German plans for invasion -- even the scaled back ones. They would have been too thinly stretched and even our battered army would have inflicted sufficient casualties on the beaches to have probably stopped an invasion in its tracks. Parachutists would have made a difference, but in somewhere as large as SE England?
Thankfully all my conjecture is just thatl!!