Afterwards, French President Emmanuel Macron said the EU would stand firm on key principles such as access to its common market and fishing quotas.
The EU has rebuffed Boris Johnson’s request to speak to Mr Macron and Germany’s Angela Merkel individually.
The UK prime minister hoped to speak on the phone to the leaders of Europe’s two largest economies but, according to EU officials, was told discussions could only take place through the bloc’s negotiator Michel Barnier.
Speaking after Mrs von der Leyen’s latest comments, Mr Johnson said a no deal outcome was “very likely” in the coming days unless there was a “big change” from the EU.
Time is running out to reach an agreement before the UK stops following EU trade rules on 31 December.
Weeks of intensive talks between officials have failed to overcome obstacles in key areas, including competition rules and fishing rights.
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Mrs von der Leyen, who met Mr Johnson on Wednesday for three hours of talks, has briefed European leaders, who have just held a two-day summit in Brussels.
According to EU officials, she struck a downbeat note about the chances of success, saying the “main obstacles” standing in the way of a deal – disagreements over fair competition rules, how a deal would be enforced and fishing quotas – remained in place.
She later told reporters that the two sides’ positions “remained apart on fundamental issues”.
The EU is determined to prevent the UK from gaining what it sees as an unfair competitive advantage from having tariff-free access to its markets but the ability to set its own standards on products, employment rights and business subsidies.
Mrs von der Leyen said the UK would not be required to “follow” every new rule or product standard imposed by the EU after 31 December.Boris Johnson says there is a “strong possibility” the UK will not reach a post-Brexit trade deal with the EU.
But if the UK decided to go its own way on some rules, there would be a price to pay with possible tariffs, she added.
“We have repeatedly made clear to our UK partners that the principle of fair competition is a pre-condition to privileged access to the EU market,” she said.
“It is the largest single market in the world and it is only fair that competitors to our own enterprises face the same conditions on our own market.
“This is not to say that we would require the UK to follow us every time we decide to raise our level of ambition, for example in the environmental field.
“They would remain free – sovereign, if you wish – to decide what they want to do. We would simply adapt access the conditions for access to our market accordingly, the decision of the UK, and this would apply vice versa.”
Mr Macron said the EU and UK must learn to live “side by side” harmoniously and suggested he was reluctant to give up his country’s “share” of fishing quotas from UK waters.
“I want everyone to be able to come out with the deal which on the one hand preserves the European interest and which respects our British friends,” he said.
Mr Johnson, who wants a similar deal to Canada’s 2017 agreement with the EU, said the UK had to “take back control” of its waters and not be punished if it chose not to stay aligned to EU regulations.
He said he had “yet to see” the “big offer” from the EU which could change the course of the negotiations.
“It is looking very, very likely that we will have to go for a solution that I think would be wonderful for the UK, and we’d be able to do exactly what we want from 1 January.”
- Brexit happened but rules didn’t change at once: The UK left the European Union on 31 January 2020, but leaders needed time to negotiate a deal for life afterwards – they got 11 months.
- Talks are happening: The UK and the EU have until 31 December 2020 to agree a trade deal as well as other things, such as fishing rights.
- If there is no deal: Border checks and taxes will be introduced for goods travelling between the UK and the EU. But deal or no deal, we will still see changes.
If the two sides fail to agree a deal, it could result in taxes being imposed on each other’s imports from 1 January, leading to higher prices for the goods the UK buys and sells from and to the EU, among other changes.
Mr Johnson said such an outcome “would be different from what we’d set out to achieve” but he had no doubt that the UK could do it.
Earlier on Friday, Culture Secretary Oliver Dowden suggested British farmers and car manufacturers would get extra financial support if their products were targeted.
EU prepares for no deal
The EU has set out the contingency measures it would take in the event of no trade agreement being reached with the UK.
The plans aim to ensure that UK and EU air and road connections still run after the post-Brexit transition period ends on 31 December.
They also allow the possibility of fishing access to each other’s waters for up to a year, or until an agreement is reached.
Mrs von der Leyen said they were a “short-term fix” and “one way or the other, in less than three weeks it will be new beginnings for old friends”.