THERESA May has insisted that her Brexit plan is the best one for jobs across the UK as she battles to keep her own job in Number 10 during another crucial week for her premiership.

In a message to her political rivals, the Prime Minister stressed that Brexit was not an exercise in "political theory" but something that affected people's lives and livelihoods.

In Brussels, Michel Barnier, the European Union's chief negotiator, said the Brexit process was at a "key moment" and urged all sides to remain "calm".

One of the remaining details to be resolved is how long a possible extension to the transition period - effectively keeping the UK aligned with the EU after Brexit - could last for. This is an option because, in theory, it would help avoid having to have a backstop period.

Intriguingly, Greg Clark, the Business Secretary, talked up the prospect, saying it had “option value”.

There has been speculation that a one-off extension, if sought when the agreed transition period expired at the end of 2020, could last until the end of 2022.

Mrs May conspicuously did not knock the idea down but stressed she would want it to be over by the time of the next scheduled general election in June 2022, while Mr Barnier said an extension could not be "indefinite" and a deadline would be decided in talks this week.

However, a question hangs over whether or not extending the transition would mean putting off the day the UK took back full control of its fishing waters.

At present, Britain will become an independent coastal state on Brexit Day. However, the UK Government has agreed that for the transition period the country’s fishing industry will comply with the regime of the hated Common Fisheries Policy until December 2020.

Given that quotas are set in December for the following 12 months, any extension to the transition could mean that UK fishermen would be bound by the CFP for another year. If, as Mr Barnier has suggested, the transition might extend to December 2022, this could mean the UK adhering to CFP rules until December 2023; more than seven years after the 2016 vote to leave the EU.

Any extension to the transition that meant UK fishermen continuing to abide by CFP rules would be anathema to Scottish Conservatives, who have threatened to vote against Mrs May’s proposed deal, if this were the case.

But it has been suggested the draft withdrawal agreement “kicks the can down the road” as it simply says on the future of fisheries that both sides would use their “best endeavours” to come up with what happens beyond December 2020 with an agreed plan by July 2020.

Mr Barnier and others have flagged up the possibility of slapping tariffs on UK fishing products if there is no guarantee of continued access for EU boats to UK waters.

This morning, the PM took her Brexit message to the CBI conference as she sought to win business backing for her plans.

CBI director-general Carolyn Fairbairn told the event in east London: "It is a compromise. But it is hard-won progress."

She said firms were already spending hundreds of millions on preparations for a no-deal Brexit.

In her keynote speech, Mrs May said: "We are not talking about political theory but the reality of people's lives and livelihoods. Jobs depend on us getting this right.

"And what we have agreed unashamedly puts our future economic success, and the livelihoods of working families up and down this country, first."

But Brexit-supporting businessman Roger Kendrick challenged her over her plans, which he said would restrict the ability to strike trade deals with countries outside the EU, telling Mrs May: "Think again about the economics of the whole thing."

The PM told him: "The portrayal that you have given of what has been agreed is a little inaccurate," adding: "It makes sense for us to continue having a good trading relationship with the European Union...but also have the freedom, which we will have, to sign those trade deals around the rest of the world."

In Brussels, Mr Barnier updated ministers from the 27 remaining EU nations on the state of the Brexit process.

Austrian EU minister Gernot Blumel said it was "a painful week in European politics" and "we have the divorce papers on the table, 45 years of difficult marriage are coming to an end".

Luxembourg's foreign minister, Jean Asselborn, said: "This deal that is now on the table is the best there is. There is no better deal for this crazy Brexit."

Asked if he thought Mrs May could survive, Mr Asselborn said: "I believe she can convince her party and perhaps a part of parliament which is not on her side, so that this deal can become reality."

The question of Mrs May's survival is one that the EU27 are watching closely as Tory rebels continued to attack her plan although there still remained doubt as to whether or not they had the 48 signatories needed to spark a no-confidence vote. A total of 23 have gone public. Some MPs who were said to have put in letters to Sir Graham Brady, who chairs the 1922 backbench committee, refused to confirm publicly they had done so.

The message from both the PM and the EU27 representatives in Brussels was that there could be no unpicking of the divorce deal, although work on the blueprint for the future relationship continues.

Mrs May made clear the proposed withdrawal plan had been "agreed in full" by both sides.

However, David Davis, the former Brexit Secretary, said: "This deal is not what the people voted for. It will tie us to the customs union for years to come with no way out.

"But there is still time to negotiate a Canada+++ deal that delivers on the referendum. So let's get on with it."

And Boris Johnson, the former Foreign Secretary, made yet another colourful attack on her plan.

He used a column in Monday's Telegraph to describe the agreement as a "585-page fig leaf [that] does nothing to cover the embarrassment of our total defeat".

Calling for the scrapping of the Northern Ireland backstop, he added: "We should massively accelerate our preparations to exit on World Trade Organisation terms, with a new Secretary of State responsible for all the cross-government work.

"There would, of course, be some disruption in that outcome, but by no means as much as sometimes predicted.

"And it is our failure to make proper preparations that has so gravely weakened our negotiations."