Michel Barnier has hit out at the “tone” of Boris Johnson’s Europe adviser David Frost, as the row between the UK and European Union over post-Brexit trade talks continued to simmer.

The European Union’s lead negotiator said a “new dynamism” was needed in talks if they are to avoid a “stalemate”.

He was responding to a letter from Mr Frost, which was highly critical of the EU’s approach to the negotiations.

Mr Frost’s letter followed the latest round of negotiations on a trade deal, which made little progress and were described as “tetchy” by British insiders.

Sticking points in the talks include the EU’s call for access to British fishing waters and “level playing field” conditions on areas such as state subsidies, workers’ rights and environmental protections.

In his letter on Tuesday, Mr Frost said Brussels’ proposed deal “contains novel and unbalanced proposals which would bind this country to EU law or standards”.

“What is on offer is not a fair free trade relationship between close economic partners, but a relatively low-quality trade agreement coming with unprecedented EU oversight of our laws and institutions,” he said.

In his reply, Mr Barnier said he did not think “an exchange of letters regarding the substance of the negotiations is necessarily the best way to discuss on substantial points”.

He added: “It cannot be a substitute for serious engagement and detailed negotiations and, in particular, I would not like the tone that you have taken to impact the mutual trust and constructive attitude that is essential between us.”

The UK has insisted it wants a trade deal along the lines of that struck with Canada, and fishing arrangements similar to those of Norway.

But Mr Barnier said the EU would not accept “cherry picking” of elements of previous deals the bloc has struck.

On the level-playing field commitments, Mr Barnier said the UK “cannot expect high-quality access to the EU single market if it is not prepared to accept guarantees to ensure that competition remains open and fair”.

He also warned that time was too tight – with the UK committed to the end-of-year deadline – for the kind of trade deal sought by Mr Johnson.

“Apart from the fact that we do not have necessary time for a negotiation on each tariff line, the EU has always made clear that any future trade agreement between us will have to include strong level playing field guarantees, irrespective of whether it covers 98% or 100% of tariff lines,” he said.

The Prime Minister is prepared to walk away from talks if progress is not made by the time of a high-level summit in June.

Mr Barnier said there needed to be “tangible” progress across all areas of negotiation – including on the level playing field, fisheries and the governance of the arrangements.

Ahead of the next session of talks in the week of June 1, Mr Barnier said: “The next round must bring this new dynamism in order to avoid a stalemate.

“I remain convinced that with mutual respect and constructive engagement by the UK across the board, on all issues on the negotiating table, we can move forward in the limited available time.”

Mr Barnier’s response to Mr Frost came after Spain’s foreign minister called for both sides to show flexibility.

Arancha Gonzalez Laya said: “The most important thing now is to stop posturing, stop sending letters, to stop sending emails, sit down and negotiate – that’s what we need to see now.”

She told BBC Radio 4’s Today programme: “I think both sides have to show flexibility, it’s not as if this was a one-way street.

“There is clearly a desire on the British side to continue to enjoy the benefits of belonging to the European internal market, very certainly, and that has to come with a price because Britain will no longer be a member of the European Union.

“You can’t be out and still enjoy the benefits as if you were in. On the European Union side, there are a number of things that are important to the European Union – fishing is one of them.

“What we need to see happening now is a real negotiation and no posturing, it’s too late for this.”