In England, can I buy fresh fish directly off the boat?
Brixham is a traditional fishing port in Devon. Their fish market is a (mainly) wholesale operation but lists local sellers, one of which is the actual boat selling at the quayside (the link on that page is broken). Unfortunately for you, even if you're within essential travel range of Devon at the moment the boat appears to be undergoing a refit.
This does demonstrate that it's possible/legal, even if you're nowhere near Brixham.
It's rare though. There's a directory of "direct" sales (their word), some of which might be of interest (e.g. see what's been caught, have it prepared and delivered).