A trade deal between the UK and European Union is still possible, Brussels’ chief negotiator Michel Barnier has insisted.

Talks were extended on Sunday after Boris Johnson and European Commission president Ursula von der Leyen agreed to continue the process despite major differences still remaining.

Mr Barnier updated diplomats from the 27 EU states about the progress which has been made before resuming negotiations with his UK counterpart Lord Frost.

For months the talks have been deadlocked on the issues of fishing rights and the “level playing field” to ensure that neither side can unfairly compete with the other on environmental standards, workers’ rights or state subsidies.

Mr Barnier confirmed that those remain the main issues, telling reporters in Brussels “two conditions are not met yet” but “this deal, it is still possible”.

The other issue which has dogged the negotiations – the legal mechanisms to govern any deal – was not mentioned by Mr Barnier, suggesting those difficulties may have been resolved.

Mr Barnier said the “next few days” are important if a deal is to be in place for January 1.

“It is our responsibility to give the talks every chance of success,” he said.

“Never before has such a comprehensive agreement (trade, energy, fisheries, transport, police and judicial co-operation etc) been negotiated so transparently and in such little time.”

A spokesman for the grouping of EU ambassadors said there is “full support for the resilient and persistent” negotiating team led by Mr Barnier.

The UK’s current trading arrangements with the EU expire at the end of the month, meaning any new deal would have to be in place by January 1.

If not, tariffs and quotas will apply and bureaucracy will increase, causing further damage to an economy already ravaged by coronavirus.

Irish premier Micheal Martin said it will be difficult for the EU and UK negotiating teams to “square the circle” to reach a post-Brexit trade deal.

But the Taoiseach said both sides are aware of the “enormity and severity” of a no-deal Brexit on their respective economies.

“They have really sought to crack the level playing field issue along with fisheries and, crucially, this dispute mechanism that would underpin any level playing field framework,” he said.

The need for any deal to be approved by Parliament means that talks cannot continue right up until New Year’s Eve, but MPs are braced for the prospect of sitting over the festive period.

Business Secretary Alok Sharma told the BBC: “We have always said the transition period ends at the end of December and we will not be continuing discussions beyond that.

“Any deal that we have will then have to go through Parliament, so that would really be cutting it quite fine.”

But he added that Parliament “can move very quickly” to approve a deal if it had to.

Former chief whip Mark Harper, speaking to BBC Radio 4’s Westminster Hour, said: “Many of us are fully anticipating it’s entirely possible we might be returning to Parliament between Christmas and New Year to scrutinise this and vote it through if a deal is done.”

Downing Street repeatedly refused to guarantee that MPs would be given a vote on a deal before it came into force.

The Prime Minister’s official spokesman said it was a matter for Commons Leader Jacob Rees-Mogg but added: “We are confident that there is time to do whatever we need to do in Parliament.”

Sunday’s deadline for a decision on the future of the talks saw Mr Johnson and Mrs von der Leyen agree to “go the extra mile” in search of a solution.

Mr Johnson, speaking after the call, said the UK would not be walking away from the negotiating table and that “where there is life, there is hope”.

But he continued to warn that a no-deal outcome is still the most likely scenario.

He said the country should get ready for the breakdown of talks, resulting in tariffs under World Trade Organisation (WTO) terms from January 1 – a move that is predicted to cost jobs, cause food prices to rise and wipe £45 billion off the economy next year.

“The most likely thing now is, of course, that we have to get ready for WTO terms, Australia terms,” the Prime Minister said.

There will be a deal one day between the United Kingdom and the European Union, there is no doubt about it. If mindsets are ready for a deal in London, well, let’s celebrate. If they are not, then we’ll talk again next year

French MEP Nathalie Loiseau, an ally of President Emmanuel Macron, suggested that a no-deal scenario would simply lead to more talks in 2021.

Speaking on BBC Radio 4’s Today programme, she said: “If there is any chance to reach a deal we will not let it go.

“There will be a deal one day between the United Kingdom and the European Union, there is no doubt about it.

“If mindsets are ready for a deal in London, well, let’s celebrate. If they are not, then we’ll talk again next year.”

Downing Street has repeatedly ruled out negotiations continuing in 2021.

Optimism around the continuation of the talks on Monday was reflected in the currency markets.

“Sterling has rallied 1.2% to 1.3390 versus the US dollar as markets showed some relief that EU trade talks haven’t collapsed,” said Russ Mould, investment director at AJ Bell.