I think the problem with that was that they lost the early warning radars and could not scramble fighters from anywhere nearby, so that would have forced the RAF to fly combat patrols over the east, taking away some advantages they had before. The plans for the invasion were mostly delayed because of the Royal Navy, which could have sunk all the invading ships or all the supply ships required to sustain an invasion. The german air force however did not seem capable of stopping the Royal Navy even with air superiority over the channel.
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