Consumers are "completely confused" about whether or not they can eat cod with a clear conscience, despite it being the second most popular fish in the UK.
The North Sea cod fishery collapsed in the 1980s as a result of overfishing but recently rose above dangerously low levels for the first time after years of reduced fishing and efforts to avoid catching cod in mixed fisheries.
The signs of improvement led the Marine Conservation Society, which assesses seafood on a traffic light system and a 1-5 rating where one is the most sustainable, to raise the fishery to an "amber" rating and a level 4 recommendation that it should be eaten only very occasionally.
But a new survey by the Marine Stewardship Council (MSC), the ecolabel for sustainable seafood, found 35% of adults did not know if cod was sustainable or if they should be eating it.
Almost three in 10 consumers (28%) thought there were plentiful and sustainable supplies of cod but the same number believed the opposite was true and people should actively avoid eating it where possible.
But the confusion was not reflected in sales, with UK consumers eating an estimated 72,898 tonnes last year, second only to salmon.
MSC programme director Toby Middleton said: "It's no wonder that a lot of people are completely confused about cod.
"Over the last decade, campaigners have been telling people to avoid eating cod from the North Sea, and other places where it's been overfished.
"That has stuck in people's minds, but it doesn't mean you need to avoid all cod - it can be sourced sustainably from Icelandic or Norwegian waters, for example.
"As a shopper or diner, it can be hard to remember what's sustainable and what isn't, but the simple way for shoppers to tell if cod has been sustainably sourced is to look for the MSC ecolabel, as it gives an independent assurance that it was fished responsibly and is traceable from ocean to plate."
Earlier this month, a Danish fishery began assessment for MSC certification for its North Sea cod and Scottish fisheries have also expressed an interest in achieving MSC certification for their North Sea cod catch, the organisation said.
Mr Middleton said: "All being well, MSC certified North Sea cod landed on British shores could be back in British shopping baskets within a couple of years."