Michel Barnier has spoken of grave differences between the EU and the UK over their future relationship, warning that Boris Johnson’s refusal to formally commit to the European convention on human rights would limit cooperation in fighting crime.

Following the first round of negotiations between the two 100-strong teams, the EU’s chief negotiator said there were many “serious divergences” between the two sides.

The problematic areas were said to range from the maintenance of a level playing field for British and European businesses to the role of the European court of justice and conditions on future access for European fishing fleets to British waters.

In response, a UK government spokesman said there were “expected, significant differences” but that the final deal had to respect that the country would be outside the orbit of EU law or its courts.

As he ran through the main obstacles to a deal, Barnier warned that the British position on the role of European courts threatened “the level of ambition of our cooperation” on joint work to fight crime, terrorism and money laundering.

He said the UK had informed him that “they do not wish formally to commit to continuing to apply the European convention on human rights, nor do they wish to permit the European court of justice to play its full role in interpreting EU law”.

Barnier said that on issues such as the exchange of personal data, including DNA, the UK’s formal commitment to the convention on human rights and the recognition in any trade deal of the role of the court of justice as the arbiter of EU law was a “must have”.

“This is serious, I say this is grave, because if the United Kingdom’s position does not move it will have an immediate and concrete effect on the level of ambition of our cooperation,” he said.

The British government has not said it will quit the European convention on human rights but it does not believe the EU should demand obligations in a treaty beyond that agreed by other independent countries.

Boris Johnson’s government also insists that there should not be a role for the European court of justice within any future treaty, while accepting that the court interprets EU law for member states.

A UK source close to the negotiations said the government’s “determination to regain independence did not compromise our commitment to high standards in all areas” including in human rights.

“But that doesn’t mean that we can accept a relationship that limits our freedom to legislate in those areas or enforce the supremacy of the law,” the source added.

On the EU’s demand that any free-trade deal must involve signing up to current European regulations on environment, workers’ rights and state aid for companies, British negotiators have said they intend to maintain high standards but oppose making them a precondition for a trade deal.

“Whilst we agree on preserving high standards, my question is why not commit to them formally? It is a question of trust,” Barnier said.

He added that he had been “quite surprised” to see the UK mandate for negotiations with the US, in which the government is vowing it will not water down standards.

“I was very interested to see that there was this element of the level playing field,” Barnier said. “Of course it’s a different context, different proximity, geographic and economic proximity. But the philosophy … is the same. We will need an agreement on the level playing field to guarantee that that was promised by Boris Johnson and the European leaders in the political declaration [to] avoid any unfair competitive advantages.”

The British government has said the commitments it is willing to make to avoid distortions in trade through undercutting standards are similar in both deals.

On fishing rights, Barnier said the UK’s proposal to negotiate the level of catches in British waters on an annual basis, similar to an agreement with Norway, was impractical. He noted that the EU and Norway negotiated over five species of fish while there were 100 shared stocks in European and British seas.

Barnier said the British government was further insisting that fisheries should be outside the main trade deal. “An economic agreement with the UK will have to include a balanced agreement on fisheries,” he insisted.

A UK government source described the EU’s negotiating ask as being “the status quo”. “That is not going to happen”, the source added.

The two sides are also at loggerheads on the nature of the agreement they are seeking. The EU wants one over-arching agreement covering everything from trade to transport, fisheries to agricultural standards, underpinned by a common dispute-settlement system.

The UK wants a series of mini-deals that have different arrangements for resolving disputes when needed. Barnier said the EU’s preferred “association agreement” model was “not a matter of ideology” but a “practical question”.

The EU is concerned that having multiple deals will make ratification more difficult with national parliaments seeking a say. Despite the differences, Barnier said he remained confident that a deal was possible by the end of the year.