Everybody should try and use thier local fishmonger. The fish tends to be fresher and there is always a great selection. Eddie's Seafood Market is just down the road from me and I try to go there every week. Located on Roseneath Place in Marchmont, South Edinburgh, Eddie has been selling great fish since there 1986.
To find a good fishmonger near you try this link to the UK Sushi Grade Fishmongers:
Also here is a great guide to spotting and buying the freshest fish available:
When I was there today there was a great selection on show:
herring, mackerel, Sea Bream, Plaice, Lemon Sole, oysters, mussels, wolffish (rock turbot), Salmon, haddock, monkfish, sea bass, clams,
Live crabs and lobsters.
There is always other great fish in the back that never make it out to the display so always ask if there is something specific you want.