The EU and the UK's chief negotiators have both cast doubt on a free trade agreement being concluded by the end of this year, following the latest round of negotiations.
In a statement, the UK's chief negotiator David Frost said very little progress has been made during a week of video conference talks between officials on both sides.
Mr Frost accused the EU of adopting an "ideological" approach to the negotiations, suggesting getting a deal by the end of the year was now at risk.
Mr Frost said: "I regret...that we made very little progress towards agreement on the most significant outstanding issues between us."
Michel Barnier, the EU's chief negotiator, said there were still wide gaps on the so-called level playing field issue and fisheries.
He told a news conference: "The firm position taken by EU member states is... that without a clear effective level playing field, a balanced fishing agreement, there will not be any possible agreement on our economic and trading partnership."
The EU is insisting on a level playing field in order to ensure that UK companies do not gain an unfair advantage over European exporters when accessing the single market by lowering their labour, social, environmental, taxation and state aid standards.
"We're not going to bargain away our European values to the benefit of a British economy," Mr Barnier said. "Economic and trading fair play is not for sale."
However, the UK believes the EU's demands on a level playing field amount to binding the UK to EU regulations into the future.
Mr Frost said there had been progress on other areas, but not on the level playing field. There was no real movement on the fisheries issue, he said.
"It is very clear that a standard Comprehensive Free Trade Agreement, with other key agreements on issues like law enforcement, civil nuclear, and aviation alongside, all in line with the Political Declaration, could be agreed without major difficulties in the time available. Both sides have tabled full legal texts, there are plenty of precedents, and there is clearly a good understanding between negotiators," he said.
"The major obstacle to this is the EU's insistence on including a set of novel and unbalanced proposals on the so-called level playing field which would bind this country to EU law or standards, or determine our domestic legal regimes, in a way that is unprecedented in Free Trade Agreements and not envisaged in the Political Declaration. As soon as the EU recognises that we will not conclude an agreement on that basis, we will be able to make progress.
Both sides say there was some progress on fisheries, but not enough to warrant a breakthrough.
The UK is insisting on restoring full control over its territorial waters. The EU wants to maintain, as far as possible, the level of access EU fleets enjoyed while the UK was a member, on the basis that such access was based on agreements that in some cases went back centuries.
The UK has accepted that EU fleets will have continued access, but it wants that access to be determined on an annual basis, such as the arrangement currently in place between the EU and Norway.
The EU wants quota shares to be agreed for the long term, and not annually, pointing out that it shares only seven species with Norway, and over 100 with the UK.
Both sides have indicated they believe the other must move if the talks are to succeed. The UK will leave the transition period at the end of December, and if no free trade agreement has been concluded, both sides will have to trade on WTO terms, meaning tariffs, quotas and other non-tariff barriers to trade.
"We very much need a change in EU approach for the next round beginning on 1 June," Mr Frost said in a statement.
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The EU has accused the UK of seeking to cherry-pick the best parts of the EU's trade deals with Japan, Canada and South Korea.
Mr Barnier said: "The EU wants an unprecedented forward-looking agreement, not a narrow one rooted in past precedents and sliced up sector by sector."
Mr Barnier also urged the UK to fully implement the Protocol on Northern Ireland.
He said: "The solution we agreed with the UK ensures continued peace and stability on the island of Ireland and upholds the Good Friday/Belfast Agreement in all its dimensions.
"The agreement preserves the EU single market by ensuring all the necessary checks and controls on goods entering Northern Ireland from Great Britain or anywhere else. All those who pursue these objectives must now also correctly implement the protocol, the system needs to be fully operational on 1 January next year.
"This is a stable and lasting solution subject to a process of ensuring democratic consent of the majority of the elected representatives in Northern Ireland's legislative assembly."