The council, which certifies whether fish are being caught sustainably, says it is too soon to tell exactly when the North Sea fishery will be sustainable. But a spokesman said on current trends, it will be ready for certification within years rather than decades.
Stocks would still be in recovery then, James Simpson said, but they would have passed an acceptable level. MSC certification is determined by the state of the stocks, the environmental impact of the fishery, and if there is a management system in place to maintain sustainability if circumstances change.
The latter two were already in place, Mr Simpson said.
"This is really great news," he said. "We have done an assessment of the entire inshore industry and it's clear that cod is on the way back." The recovery was thanks to strict catch limits aided by a massive public campaign for sustainable fish, he said.
Barrie Deas, the chief executive of the National Federation of Fishermen's Organisations, which represents fisherman in England, Wales and Northern Ireland, told Radio 4's Today programme it was a "dramatic turnaround".