But it warned that the UK industry should not discard elements of the CFP which have helped maintain stocks and prevent over-fishing, the Press Association reported.
And it noted that the UK will continue to be under international obligations to co-operate with neighbouring states where fish stocks are shared between the waters of two or more countries
Lord Teverson, chairman of the Lords EU Energy and the Environment Sub-Committee, said: “Many people in the UK fishing industry were vocal supporters of Brexit and there is a strong sense that it presents an opportunity for them to grow and develop the industry.
“That may very well be the case but if that opportunity is to be taken, while ensuring fishing does not return to the unsustainable levels of the past, we need to ensure the recent positive developments of the Common Fisheries Policy, largely promoted by the UK, are not discarded.
“Fish stocks are a shared resource and fish don’t recognise national borders. We will have to continue managing fish stocks in a responsible and co-operative way to prevent over-fishing.
“The UK fishing industry relies heavily on trade with the EU.
“Brexit will involve many trade-offs, and it may very well be that EU member states demand more access to UK waters than some fishers would want in return for our continued rights to sell fish to the European market with zero tariffs.
“What we are absolutely clear on is that the fishing industry and the coastal communities who rely on that industry should not be overlooked and must be fully consulted.
“While fisheries is a relatively small part of the UK economy, it is of fundamental importance to a great many people in different parts of the UK, from Brixham to Grimsby and Newlyn to the Shetlands. Those voices must be heard in the negotiations.”