We're bringing our live coverage of today's events to a close, but here is a quick catch-up on developments:

• Boris Johnson and the European Commission president Ursula von der Leyen committed to further negotiations on a post-Brexit trade deal between the UK and EU, pledging to "go the extra mile"
• It came after the two sides agreed an initial deadline for progress - the transition period ends formally at 23:00 GMT on 31 December
• Speaking to broadcasters, the PM said "we're still very far apart on key things" - as talks are scheduled to continue in Brussels this week
• Johnson said he thought there was "a deal to be done" if the EU wanted to do it - but did not strike an optimistic tone
• Business groups criticised the continued uncertainty, saying firms were finding it extremely difficult to prepare for 1 January
• Senior Conservatives backed the PM to keep talks going but not accept a deal at any cost
• Labour called on Johnson to "get us the deal" so the UK can "move on"

Our writers and editors today were: Alex Therrien, Lauren Turner, Gavin Stamp, Justin Parkinson, George Bowden and Julian Joyce.

Thanks for reading.

The Scottish government has called for an end to the "crippling uncertainty" over the future trading relationship with the EU.

It comes after European Commission President Ursula von der Leyen and UK Prime Minister Boris Johnson today agreed that post-Brexit trade deal talks will continue this week.

The Scottish government's Cabinet Secretary for Europe and External Affairs, Michael Russell, said: "It is now time for the crippling uncertainty over the future of our trading relationship with the European Union to come to an end.

"Whatever the outcome of these protracted talks, we know there will be very significant damage to Scotland's economy and society because of the UK government's decision to leave the transition period on 31 December in the middle of a pandemic and a recession.

"But we also know that the worst outcome of all would be the disastrous impact of a no-deal Brexit - which would lead to significant tariffs - and the UK government must rule this out immediately."

Image source, Getty Images

The CBI, the UK's business lobby group, says that news the UK and the EU will continue Brexit talks gives it hope.

But it says: "Ongoing delays are frustrating and cost businesses."

The CBI says the UK government must, firstly, provide detailed guidance to businesses this week on issues such border checks.

Secondly, companies must be given a grace period to allow them to adjust to a deal or no deal.

"And third, prepare support for firms who will face the greatest challenges in the short run. Those in sectors and supply chains that are badly hit will face extinction through tariffs, red tape and extra costs."

Image source, Getty Images

As talks about how the UK and EU could live and work together after Brexit near a mutual deadline, let's take a look at some of the language being used.

Politicians use many different terms when discussing Brexit - from transition period to WTO.

Here is what some of the key ones mean.

Laura Kuenssberg
Political editor

Image source, Andrew Parsons / No 10 Downing Street

When is a deadline not a deadline? When it's anything to do with Brexit, perhaps.

Both sides in this long, long process, have agreed to go on, rather than pull the plug today.

A joint statement emerged just before noon with a much more positive tone than anything that's come out of late, and did not feature the usual kind of warning of big gaps between the two sides.

The froideur from Thursday and Friday seems to be thawing a little. It's worth noting no new time limit was put on the talks, although of course there is one hard deadline of 31 December, when the status quo runs out.

It's also worth noting that the prime minister was loathe to show much sign of optimism when he appeared in front of a camera shortly after the joint statement emerged.

It's far from certain that the talks will end in agreement, but the chances of resolution are once again on the rise.

Read more from Laura here.

Simon Jack
BBC Business Editor

Image source, Getty Images

This torture is better than no deal.

The fact that talks are ongoing is a good thing. Business groups are unanimous in their view that if a deal is at all possible, it should be pursued with every last effort.

However, the problem with this uncertainty torture is two-fold.

First, political and business timetables are getting increasingly misaligned by the day. Businesses need to know whether tariffs are coming or not as it effects pricing of products and services for next year. How can I place or take an order if I don’t know what that price needs to be?

Second, there is a danger that businesses who watch this process being dragged out will wait for some rabbit to appear out of the hat and take their focus away from preparing for a deal. No deal is very bad - a deal still leaves an awful lot of work to do in preparing for new procedures, for example customs, that will change whether we get a deal or not.

But the fact remains that while this may be torture, it could be worse.

No deal would not put UK business out of its misery – it could put some sectors out of business.

A few moments ago, Prime Minister Boris Johnson gave an update on the post-Brexit trade deal discussions between the UK and the EU after both sides agreed to continue talking.

He cautioned that the two sides were "very far apart on key things", adding that the most likely outcome was no deal.

We've been telling you about Prime Minister Boris Johnson's call with European Commission President Ursula von der Leyen.

He later briefed members of the Cabinet from his office at 10 Downing Street - and now a picture of the PM giving that briefing has been released.

It was taken by his photographer Andrew Parsons.

Image source, Andrew Parsons / No 10 Downing Street

Image source, Getty Images

A continuation of Brexit talks is not all good news - uncertainty means that businesses such as retailers are finding it extremely difficult to prepare for 1 January.

The British Retail Consortium (BRC) says that, without a deal, UK shops face £3bn in tariffs and those extra charges could be passed onto customers.

BRC chief executive Helen Dickinson, said: "Both sides must double down and do what is necessary to agree a zero-tariff agreement, or else it will be the public that pay the price of this failure.

"With many people’s finances already strained by the economic impact of coronavirus, households can ill-afford a significant rise in food prices.

"For the sake of customers and businesses around the UK, we need a deal in the next three weeks.”

Prime Minister Boris Johnson said there was still a deal to be done "if our partners want to do it - but we remain very apart on these key issues".

He said: "The UK can’t be locked into the EU’s regulatory orbit and we’ve obviously got to take back control of our fisheries, so those are the points - I think it’s very clear what the UK is talking about."

Mr Johnson said the UK "certainly won’t be walking away from the talks", reiterating what Ursula von der Leyen said, that "people would expect us to go the extra mile".

He said he repeated his offer to talk to "other capitals" but said the Commission was "very determined" to keep the negotiations between the UK and Commission.

Mr Johnson said the UK had made "huge preparations" to leave without a deal.

"We’ve now been at this for four and a half years, it’s a long time. Perhaps more intensively in the last couple of years than previously.We’ve got ready and anybody who needs to know what to do, get on to gov.uk/transition, external, see what needs to be done and get ready for 1 January.Either way, whatever happens the UK will do very very well."

Image source, Getty Images

In his statement earlier Boris Johnson warned the UK had to "get ready for WTO terms, Australia terms", if the current talks with the EU do not succeed.

To be clear, an Australian-style Brexit would mean no trade deal with the EU and would see the UK trading instead under the rules of the World Trade Organization (WTO).

But what does that mean? Read more here.

"Get ready with confidence for 1 January - trading on WTO terms if we have to," Johnson says in his statement.

"Get ready to trade on WTO terms - and there is a clarity and a simplicity in that approach which has its own advantages," he says, adding: "It's not where we wanted to get to."

"We're going to try with all our hearts," he says of the ongoing negotiations for a trade deal.

Speaking to broadcasters, Prime Minister Boris Johnson says "we're still very far apart on key things" as post-Brexit trade talks continue in Brussels.

He says he is "very happy" to speak with other European capitals, and he repeats: "The most likely thing now is that we have to get ready to WTO terms - Australia terms."

Earlier, the PM held a cabinet call following talks this morning with EU Commission President Ursula von der Leyen.

Following those talks, the EU and UK issued a joint statement confirming negotiations to reach a post-Brexit trade deal would continue.

The Times’ political editor, Steven Swinford, has just tweeted, external a read-out from the cabinet call, saying the PM sounded "downbeat" about the chances of reaching a deal.

Labour has urged the UK government to seal a trade deal with the EU after the two sides agreed to carry on negotiating.

A party spokesman said: "The Conservatives promised the British people that they had an oven-ready deal and that they would get Brexit done.

"The government needs to deliver on that promise, get us the deal and allow us to move on as a country."

The British Retail Consortium (BRC) has also warned people not to start stockpiling goods ahead of 1 January.

“Retailers are doing everything they can to prepare for all eventualities on 1 January - increasing the stock of tins, toilet rolls and other longer life products so there will be sufficient supply of essential products," says BRC chief executive Helen Dickinson .

"While no amount of preparation by retailers can entirely prevent disruption there is no need for the public to buy more food than usual as the main impact will be on imported fresh produce, such as fresh fruit and vegetables, which cannot be stored for long periods by either retailers or consumers."

Charles Michel, the president of the European Council, has said the European Union would not lose its cool as make-or-break talks with Britain over a post-Brexit trade deal approach their climax.

Michel, who chairs EU summits, told France Inter Radio that the EU wanted a good deal that respected the integrity of its single market, the Reuters news agency reports.

European Commission President Ursula von der Leyen has confirmed that talks for a post-Brexit trade deal will continue between the UK and EU.

She said "despite the exhaustion after almost a year of negotiations", it was "responsible to go the extra mile".

Kevin Connolly
Europe correspondent, Brussels

Ursula von der Leyen described her call with Boris Johnson as "constructive" and "useful".

She used Imperial measurements when she talked about "going the extra mile", perhaps a nod to the British side.

And there is no apparent deadline now - I think they may have felt that that created the wrong impression of what would happen today.

As long as both sides are talking then a deal is certainly not impossible and it would have been impossible had they pulled the plug today.