Lars Løkke Rasmussen, whose country catches more than a third of its fish in British waters, said Denmark would push for a “balanced deal” in which a share of UK fishing rights are on the table, risking further ire from fishermen already angry at the terms of a 21-month transition deal agreed by the UK this week.

Bertie Armstrong, the chief executive of the Scottish Fishermen’s Federation, flatly dismissed the suggestion that fishing could be offered up in exchange for a trade deal with the EU, saying Denmark and its neighbours could “think again”.

Last night, Mr Rasmussen said fishing “is a priority for my country, of course”.

Denmark's Prime minister Lars Lokke Rasmussen arrives on the first day of a summit of European Union (EU) leaders at the EU headquarters in Brussels. Picture: Getty Images

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The Danish Prime Minister told the BBC: “I think it’s 30 per cent to 40 per cent of the total value in the Danish fisheries sector, which is caught on British waters. So this is of course a high priority.

“This is negotiation, we have to close a balanced deal.”

Responding to Mr Ramsmussen’s comments, Mr Armstrong told The Scotsman: “They would say that, wouldn’t they? They can think again.”

British Prime Minister Theresa May (L) arrives at the Council of the European Union..(Photo by Jack Taylor/Getty Images)

The Conservative MEP from Scotland Baroness Nosheena Mobarik said there was “no reason to give access to our waters” in trade talks with the EU.

“It’s not part of a trade agreement,” she said.

Theresa May said she was hopeful of a “swift” move to trade talks with the EU as she arrived for a summit in Brussels.

Leaders of the remaining 27 EU nations are today expected to give their approval to a draft agreement on the terms of the UK’s withdrawal from the EU, including a post-Brexit transition period lasting until the end of 2020.

European Council president Donald Tusk has recommended endorsement of the deal, which he said would put off “the negative consequences of Brexit” for another 21 months after the formal date for the UK’s withdrawal in March 2019.

Arriving at the European Council summit, Mrs May said she was “looking forward to talking about Brexit,” adding: “We made considerable progress through the agreement on the implementation period, which will bring certainty to businesses and people.”

However, 13 Conservatives and one DUP MP have signed a joint letter threatening to vote down the final Brexit deal unless the Prime Minister tears up “unacceptable” proposals for fishing.

They commit the UK to remain bound by Common Fisheries Policy quotas until 2021.

Glasgow Shettleston SNP MSP John Mason warned this would be a “red line” for the SNP, despite the party’s stated policy of seeking to remain in the EU.

Mr Mason said an independent Scotland would not rejoin the EU if it meant a bad deal for the country’s fishing sector, in an apparent breach with party policy.

He wrote on Twitter: “Scotland would not rejoin EU if we did not get a good deal for our fishing sector. That would be a red line, deal breaker.

“By contrast, fishing is not important for Westminster, so they have and will bargain fishing rights against higher priorities like Gibraltar.”

The issue was raised at First Minister Questions in Holyrood yesterday where Nationalist Banff and Buchan MSP Stewart Stevenson said there was widespread “anger” among fishing communities.

Ms Sturgeon said: “What we have seen this week is a broken promise and a complete betrayal by the Scottish Tories of the Scottish fishing industry.

“It is disgraceful. It’s only a week or so ago that Ruth Davidson was issuing press releases co-authored with Michael Gove of all people, saying that the fishing community would be free of the Common Fisheries Policy by March next year.

“Now we find out that we will still be governed by the Common Fisheries Policy, but to add insult to injury, there will be no vote around the table for the Scottish fishing community. It is utterly disgraceful.”

Brexit: Danes demand right to fish in UK waters under EU deal