Michel Barnier has rejected British demands for a Canada-style trade deal that would free the UK from EU rules as he made a thinly-veiled warning to Boris Johnson not to break his word.

Speaking in response to a landmark speech by David Frost, Britain’s Brexit negotiator, Barnier said such an offer was not on the table and noted that the prime minister had agreed only six months ago to stick to the EU’s state aid rules and current social and environmental regulations after the transition period.

Asked if Frost was right in his speech on Monday night to say that agreeing to such alignment in a trade deal would be undemocratic, Barnier told reporters: “Truly not. It is a sovereign decision of the EU, it is a sovereign decision of the UK to cooperate … That is what Boris Johnson wrote in the political declaration.”

Within hours of Barnier’s comments, the British government seized upon a change to the EU’s draft negotiating mandate, leaked to the Guardian, which sources in Downing Street suggested was an attempt to win back the Parthenon marbles for Athens.

The latest draft of the EU’s negotiating position calls for both sides to “address issues relating to the return or restitution of unlawfully removed cultural objects to their countries of origin”.

“This is just not happening,” a Downing Street source said with reference to suggestions that the language referred to the return of the ancient marble sculptures to Athens. “And it shows a troubling lack of seriousness about negotiations on the EU side.”

The Downing Street intervention came despite both Greek and EU officials insisting that the clause, proposed by Italy, Spain, Cyprus and Greece, was not related to the marbles held by the British museum but merely to a desire to stop the fraudulent movement of antiquities around Europe.

One senior EU source likened the row as throwing a “dead cat” on the table to divert attention from the fallout from Frost’s comments.

The explosion of rhetoric on both sides of the Channel offers little hope that the next 11 months of talks will be smooth.

In his speech on Monday night, Frost had set a tough line on EU demands by claiming the consent of the British public would “snap dramatically and finally” if the UK continued to be bound to the EU rulebook after December 2020. The latest EU negotiating mandate says those level playing field provisions should further develop “over time”.

Frost went on to suggest that Brussels should offer a trade deal similar to that given to Canada, which avoided any European court of justice supervision of standards or demands on “alignment” with Brussels.

Barnier’s response, and that of other EU officials, was one of polite fury. Sources said the EU negotiator had privately suggested to MEPs that the UK was backsliding on the political declaration on the future relationship signed last year.

“We have proposed a trade agreement with a country that has a very particular and unique close geographical proximity not like Canada, not like South Korea and not like Japan,” Barnier said. “Very particular. We are ready to propose and work very quickly with Britain on the basis of the political declaration, which was agreed with Boris Johnson. We stand ready to propose this agreement, if the UK wants it.”

Speaking separately, the EU’s trade commissioner, Phil Hogan, warned that the UK would bear “full responsibility” for its choices.

“We’re looking for a level playing field and they don’t seem to want it,” Hogan said. “It’s a big worry for many of the manufacturing sectors in the UK. If they want to diverge from the existing rules and regulations, we are going to have problems. And the more they diverge from the existing EU law and regulations, the more problems we’ll have.”

Guy Verhofstadt, a senior MEP and former prime minister of Belgium, who has led the European parliament’s approach to Brexit, said the UK was approaching the negotiation as if the sides were “living on two different planets”.

He added that it would be a “hell of a job” to secure a successful outcome from the negotiation given the British approach.

In response to the row over the Parthenon marbles, a spokesman for the British Museum noted the Greek government’s denial that it would pursue the statues during the trade negotiations with the UK.

The spokesman said: “The British Museum welcomes this mandate and is committed to fighting the trade in illicit antiquities across the world.

“We work in partnership with law enforcement agencies to identify and help to return objects that come into the UK illegally. The Parthenon sculptures were legally acquired and help us to tell the story of human history presented at the Museum. They are accessible to the 6 million global visitors the museum receives each year.”