As I understand it the project would be a fraction of the cost of protecting the Channel, North Sea, Baltic Sea etc piece by piece.
The Channel barrier would go somewhere from Normandy to Dorset or Devon or whatever. Then link the Scottish Islands and on to Norway. There is only one section in the North Sea that would require new technologies.
It would be eye wateringly expensive, but it would still be cheaper than doing it town by town. I think rather the point of the proposal is to open peoples eyes to the potential costs of the required sea defences.
EDIT - Wow, 23 min xpost. I got distracted. Yeah, the Norwegian trench would be the problem.
Yeah
One of the issues or consequences is how to deal with the warm gulf stream:
What happens with the warming effect of the gulf stream to NW Europe when part of the warm gulf stream no longer goes through the North Sea ?
It would make winters colder and likely summers warmer. The question is how much.
If that would be undesirable that big dike should start along the Belgium-French border (or more South), leave the Dover Strait open, and goes following the Belgium-Dutch-German-Danish coast to the North cape of Denmark and from there as separate decision to Sweden avoiding the deep part Norwegian trench but protecting an enormous Baltic coastline.
This would also keep many fishermen happier and the islander of the UK