- Video report by ITV News Political Correspondent Romilly Weeks
Theresa May is preparing to make a "bold offer" to MPs in a final attempt to get her beleaguered Brexit deal through Parliament and on to the statue book before she leaves office.
Ministers will begin discussions on Monday on a package of measures to be included in the forthcoming Withdrawal Agreement Bill (WAB) aimed at securing cross-party support.
The weekly meeting of the Cabinet on Tuesday will then consider plans for a series of "indicative votes" in the Commons to establish which proposals could command a majority in the House.
The move follows the final collapse on Friday of cross-party talks with Labour aimed at finding an agreed way forward which would allow Britain to leave the EU with a deal.
The WAB - which is needed to ratify the deal with Brussels - is expected to include new measures on protecting workers' rights, an issue where agreement with Labour was said to have been close.
However, Government sources made clear the package would not just be aimed at Labour MPs but would seek to secure the widest possible support across the Commons.
It is expected to include provisions on future customs arrangements with the EU and on Northern Ireland, including the use of technology to avoid the need for border controls with the Republic.
Labour leader Jeremy Corbyn has said his party will not support the WAB in Parliament, meaning it is likely that Mrs May will again struggle to garner the backing needed for it to pass.
"We haven't seen whatever the new Bill is going to be yet," Mr Corbyn told BBC One's The Andrew Marr Show.
"Nothing I've heard leads me to believe it's fundamentally any different to the previous Bill that's been put forward, so as of now we're not supporting it."
It will not, however, seek to re-open the Withdrawal Agreement - which included the controversial Northern Ireland "backstop" - after the EU repeatedly made clear it could not be re-negotiated.
Writing in The Sunday Times, Mrs May said: "I still believe there is a majority in Parliament to be won for leaving with a deal.
"When the Withdrawal Agreement Bill comes before MPs, it will represent a new, bold offer to MPs across the House of Commons, with an improved package of measures that I believe can win new support.
"Whatever the outcome of any votes, I will not be simply asking MPs to think again.
"Instead I will ask them to look at a new and improved deal with fresh pairs of eyes - and to give it their support."
Brexit Secretary Stephen Barclay warned that if the deal is not passed, the alternatives are not leaving the EU, which he labelled a "huge betrayal" to the democratic system, or a no-deal Brexit.
"Members of Parliament do need to face facts," he told Sky News's Ridge On Sunday.
"If Parliament won't back a deal then it needs to confront that reality and I do think we then in that instance need to bring forward our preparations to mitigate no-deal because that will need to use the additional time we have, and we'll need to move at pace to do so," Mr Barclay added.
Speaking on Sunday, International Development Secretary Rory Stewart called on Labour MP's to defy the party whip and back Mrs May's deal.
He said that if the Labour leadership was not prepared to support the Prime Minister's deal in the Commons, other "moderate, sensible" Labour MPs may do so.
Speaking on BBC One's The Andrew Marr Show, Mr Stewart also said the Conservatives and Labour are only "half an inch apart" on the terms of a Brexit deal, and suggested it still should be possible to close the gap between them.
"I don't believe there is anything that Jeremy Corbyn or we want that is that far apart," the Penrith and The Border MP said.
"If we are in the territory of a deal, where we need to focus is Parliament, and particularly getting Labour votes across. Maybe not Jeremy Corbyn's vote but there are many other moderate sensible Labour MPs."
Mr Stewart said the deal to be voted on was "bold" and offered Labour many of the things the party had been pushing for during cross-party talks.
However, Mr Stewart said the deal would not include a second referendum and said the results of the June 2016 vote must be "respected".
He continued that no-deal would be "a failure to reach a destination" and "damaging", arguing that even if the UK left the EU without a deal, negotiations with the rest of the bloc would still have to take place.
Earlier, Labour's shadow Brexit secretary said there was still a way for Theresa May to break the deadlock.
Sir Keir Starmer - going further than his leader Jeremy Corbyn - said offering the public a say on the Withdrawal Agreement Bill could yet sway enough MPs to support it.
Sir Keir told ITV News: "They could put a public vote on the face of the bill and break the impasse by saying the deal as it now is can go for a confirmatory vote to see whether the public are happy with it or not."
But, he added, that the ball was still very much in the Prime Minister's court and that Labour would assess that when they know what Mrs May is actually going to do with the bill when it's brought before MPs in the week of June 3.
"What I don't think she should do is bring forward implementing legislation to implement a deal that hasn't been passed," he said.
Sir Keir's comments came as Health Secretary Matt Hancock warned that the next prime minister should not call a general election until Britain has left the EU as it might "kill Brexit altogether".
He said going to the polls straight away could lead to Jeremy Corbyn taking over the reins at 10 Downing Street.
Mr Hancock said it was necessary for the Conservatives to deliver on the 2016 referendum result in the current Parliament before calling a general election.
His intervention comes after a number of Conservative MPs publicly expressed an interest in becoming Prime Minister over the past few days, including former foreign secretary Boris Johnson.
Among Conservative party members - who have the final say in the contest - Mr Johnson is the most popular, according to a YouGov survey for the Times.
Mr Johnson currently has the support of 39% of Tory members, while his closest rival is Dominic Raab on 13%.
Home Secretary Sajid Javid and Environment Secretary Michael Gove both have nine percent, with Foreign Secretary Jeremy Hunt on eight percent.
Mr Hancock himself is currently on one percent.
In an interview with The Daily Telegraph, Mr Hancock, who voted Remain in the referendum, said: “I think a general election before we’ve delivered Brexit would be a disaster.
"People don’t want it.
"I’m with Brenda from Bristol.
"We need to take responsibility for delivering on the referendum result."
Mrs May has said she will bring the WAB before MPs for its second reading vote in the first week of June following the short Whitsun recess.
Regardless of how the vote goes, she will then meet the chairman of the Tory backbench 1922 Committee, Sir Graham Brady, to agree a timetable to elect her successor as party leader, paving the way for her departure from No 10.
Meanwhile Tory grandee Michael Heseltine has said he will not be supporting the Conservatives in the European election, and will instead vote Liberal Democrat.
The former deputy prime minister and lifelong pro-European said the party has become "infected by the virus of extremism" and he cannot endorse its support for leaving the EU.
In an article for The Sunday Times, Mr Heseltine - who has campaigned for a public vote on the agreed Brexit deal - said: "The reason for my experiment with the Lib Dems is, of course, the Government's position on Brexit.
"I cannot, with a clear conscience, vote for my party when it is myopically focused on forcing through the biggest act of economic self-harm ever undertaken by a democratic government."
Mr Heseltine's call for the Tories to reclaim the political centre ground was echoed by former prime minister Sir John Major.