Not a barrage, but there have been tidal flow energy studies at that site. Here's one such.On a linked matter are you aware of any studies, hypothetical of course of a barrage over the 30 km at Dover?. The tidal effect would be considerable, as water would need to flow all the way around the top of Scotland...
However, the usage and importance of the shipping lanes there would I'm sure rule out a barrage, locks would probably be unable to cope with such high traffic levels.
We'd also need a much higher Thames tidal barrier and extensive high sea walls downstream too.
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