Glad you asked this, because I was thinking about posting a similar question myself concerning England.
This summer I went to the National Glass Center in Sunderland, England, right outside Newcastle. I chatted briefly with the ticket seller, who mentioned a beach where sea glass could be collected not too long a walk away. I hotfooted it over there and picked up some pieces; it wasn't very prolific on the part of the beach I walked. I later spent some time looking for sea glass at Whitby and had more luck there.
Another visitor to the Glass Center highly recommended searching at Seaham (I may not have that name quite right). What the two places have in common is a history of glass production in the area, which (the locals said) tends to mean more glass on the beach. Logical.
No one said anything about regulations prohibiting removal of sea glass, nor were there signs. I would expect prominent signage at any beach with such a prohibition.
In some long-forgotten source, I read about agates being found in western Scotland. I think it was along the firth near Inverary. Without a car, I made no effort to check that out. For me, agates would trump seaglass.
Somewhere up there--probably in northeast England rather than Scotland) is a beach where fossils can be found. I'm not a fossil person myself, but I think you'd be more likely to run into prohibitions there. The main thing, though, is that it can be very dangerous to chisel fossils out of cliffs.