Brexit negotiators Lord Frost and Michel Barnier were speaking on Monday in an effort to revive trade talks.
The negotiations are in limbo after a summit of European Union leaders last week failed to produce a breakthrough and Prime Minister Boris Johnson put the country on notice to prepare for a no-deal outcome.
Downing Street stressed that if no deal is in place by the end of the year – when the current transition arrangements end – the UK will not return to the negotiating table in 2021.
The Prime Minister’s official spokesman said: “If the EU change their position then we will be willing to talk to them.
“But they must be ready to discuss the detailed legal text of a treaty in all areas.”
EU leaders must also be committed to a resolution that “respects UK sovereignty and independence”.
“If not, we will end the transition period on Australian terms,” the spokesman said.
Business Secretary Alok Sharma has admitted that the difference between a no-trade deal outcome and “Australian terms” is a matter of “semantics”.
He told LBC: “The Australia deal is the deal that you have with countries where you are predominantly working on a WTO (World Trade Organisation) basis.”
Asked if the “Australia deal” is another term for a no-deal situation, Mr Sharma said: “It depends – you can use the phrase ‘no deal’, but the point is there is a deal.”
He added: “It’s a question of semantics at the end of the day, sure.
“There are two very clear approaches to this: we can either go down the route of doing the sort of arrangement that the EU has with Australia, the other is that we can do it down the Canada route.”
Mr Sharma said: “We have always been very clear that we want to leave on a Canada-style trade deal.”
Meanwhile, face-to-face talks took place in London on Monday morning between Cabinet minister Michael Gove and his opposite number on the UK-EU joint committee, Maros Sefcovic, to discuss issues around the Brexit divorce deal.
Mr Sefcovic said it was a “very constructive meeting” and that the EU would work until “the last minute” to get a trade deal.
The major stumbling blocks remain access for EU boats to UK fishing grounds and the “level playing field” to ensure fair competition – including any state subsidies that the Government might seek to give firms.
The developments came as the Government launched a “time is running out” campaign urging businesses to get ready for the end of the transition period on December 31, regardless of whether a trade deal is in place.
Businesses, increasingly concerned about the high tariffs of a no-deal exit, called on both sides to find a compromise for a deal.
Confederation of British Industry deputy director-general Josh Hardie warned of a “hat-trick of unprecedented challenges” from the first wave of coronavirus, its resurgence and “uncertainty over the UK’s trading relationship with the EU”.
Meanwhile, the UK’s five Anglican archbishops intervened to criticise the Government’s controversial new Brexit legislation as setting a “disastrous precedent”, in a letter to the Financial Times ahead of a Lords debate.
Led by Archbishop of Canterbury Justin Welby, they said the UK Internal Market Bill has “enormous moral, as well as political and legal, consequences” by paving the way for a breach of international law by overriding parts of the Withdrawal Agreement with Brussels.
Number 10 urged peers – including Church of England bishops sitting in the Lords – to back the UK Internal Market Bill.
“We consider the UKIM Bill to be vital,” the Prime Minister’s official spokesman said.
“It was passed with the support of the House of Commons and we believe it is a necessary legal safety net to protect the integrity of the UK’s internal market.”