It comes after environment secretary Michael Gove said the UK would leave the London Fisheries Convention (LFC), which allows vessels from six European countries to fish in UK inshore waters, within two years as a precursor to quitting the CFP.
Mr Gove said: "Leaving the London Fisheries Convention is an important moment as we take back control of our fishing policy.
"It means for the first time in more than 50 years we will be able to decide who can access our waters.
"This is an historic first step towards building a new domestic fishing policy as we leave the European Union - one which leads to a more competitive, profitable and sustainable industry for the whole of the UK."
SFF chief executive Bertie Armstrong added: “The idea that our exit initially from the London Convention and then the CFP will instantly herald a return to the old days of overfishing is preposterous and, frankly, insulting. Those who make such remarks have clearly not been looking closely at what has been going on in the industry.
“Observers and those who claim to be stakeholders in our industry need to understand that Brexit will lead to a redistribution of quotas, and not an increase.”
However, the move has been greeted with concern in some quarters, due to the lack of a clear alternative.
ClientEarth consultant Dr Tom West said: “Although this was a promise in the Conservative manifesto, triggering withdrawal from the London Fisheries Convention so soon seems to be a very aggressive negotiating tactic by Michael Gove and gives us a worrying first glimpse of what the UK’s future fisheries policy will look like.
“As a country outside the EU we need to consider how we can best co-operate with our neighbours rather than unilaterally withdrawing from all agreements in the hope that standing alone will make us better. Many fish stocks in UK waters are shared with our neighbours and so need co-operation and shared management.
“While Mr Gove talks about regaining control of fishing access and becoming responsible for fisheries management, he also needs to ensure we have strong laws which protect marine wildlife. That means laws that require effective management of the UK’s Marine Protected Areas, which protect marine life as well as fish habitats, along the same lines as the EU-derived rules currently in force.
“Withdrawing from the LFC and the CFP without any sign so far of what will replace them, is risking a rowing back on hard won environmental protections over the last 40 years.”
Mr Armstrong will hold talks with Mr Gove and DEFRA officials later this week on the future of the industry.