The prime minister is continuing to consider her next move to break the Brexit deadlock following the latest defeat of her withdrawal plan.
Senior government sources say the “ambition” is still to get Theresa May’s deal through the Commons.
But MPs will again vote on alternatives on Monday, a customs union with the EU thought to be MPs’ most likely preferred option.
Some senior Brexiteers have warned Mrs May against pursuing such a move.
Following the UK’s vote to leave the EU in 2016, Theresa May negotiated a withdrawal deal with the EU.
Although European leaders agreed to the plan, Mrs May has yet to get the deal approved in Parliament.
The prime minister has until 12 April to seek a longer extension to the Article 50 process to avoid the UK leaving without a deal.
Mrs May said the UK would need an “alternative way forward” after her plan was defeated by a majority of 58 on Friday, following earlier defeats by 230 and 149 votes.
The government has so far failed to win over 34 Conservative rebels. Remainers argue for another referendum and Brexiteers say Mrs May’s deal leaves the UK too closely aligned to Europe.
Northern Ireland’s DUP – which the government relies on for support in votes in the House of Commons – also continues to oppose the deal.
But a No 10 source indicated the prime minister would continue to seek support for her Brexit deal in the Commons and insisted efforts were “going in the right direction”.
BBC political correspondent Alex Forsyth described the cabinet as “deeply divided” over what to do next.
Speaking on Sky News, shadow foreign secretary Emily Thornberry said under a Labour government it was “likely” that the UK would leave the European Union.
She also accused the prime minister of being “out of control”, saying: “Theresa May is stamping her feet and saying I want this, no one else is allowed to do anything else.”
It “looks like the time may come” for another attempted no confidence vote in the government, she added.
If passed, this would pave the way for a general election.
The deputy chairman of the Conservative Party James Cleverly told Sky News that his party is doing “sensible pragmatic planning” in case there is a snap general election, but not seeking preparing to call one.
And speaking to the Andrew Marr show, Justice Secretary David Gauke said he did not see how a general election would solve the current deadlock.
He added that if MPs are voting in favour of a softer Brexit it would not be “sustainable” for the government to ignore Parliament.
Tory Brexiteer Steve Baker, who resigned as a Brexit minister over the PM’s handling of negotiations, wrote in the Sunday Telegraph that Mrs May’s deal “cannot be allowed to go through at any cost”.
He said the Conservative Party could split if the prime minister pursued a customs union with the EU as “it would amount to a reversal of the referendum result”.
However, he also wrote that on Thursday evening he had decided to support the withdrawal agreement before being talked out of it.
A customs union is one of the options which could be considered by MPs from all parties during a second round of “indicative votes” on Monday.
MPs are to vote on a series of options designed to test the will of Parliament to see what, if anything, commands a majority.
None of MPs’ eight proposed options secured a majority in the first set of indicative votes on 27 March, but those which received the most votes were a customs union with the EU and a referendum on any deal.
A customs union would allow businesses to move goods around the EU without checks or charges – but membership would bar the UK from striking independent trade deals after Brexit.
Labour leader Jeremy Corbyn supports a customs union, to protect the issue of avoiding a hard border in Northern Ireland.
Leading Tory Brexiteer Jacob Rees-Mogg told the Sunday Telegraph that the party needs to be led by “someone who has always supported Brexit”.
He wrote: “Now is the opportunity for the Tories to move from the current government’s position of ameliorating a bad idea that, at its highest level, it never believed in, to one that embraces it.”
Meanwhile, a number of senior MPs tipped as future Tory leaders have articles and interviews in the Sunday papers setting out their policies.
Dominic Raab, who quit the cabinet in protest at Mrs May’s handling of Brexit, explained how he would tackle knife crime in the Sunday Telegraph.
Chief Secretary to the Treasury, Liz Truss, called for the Tories to “modernise” in a wide-ranging interview in the Sunday Times.
She highlighted cutting stamp duty for young homebuyers and business tax as key policies.
Former cabinet minister Justine Greening said she “might” run for the Tory leadership.
In an interview with The Sunday Times, the Remain campaigner said the party needed a leader for the “2020s, not the 1920s”.
- Monday, 1 April: MPs hold another set of votes on Brexit options to see if they can agree on a way forward
- Wednesday, 3 April: Potentially another round of so-called “indicative votes”
- Wednesday, 10 April: Emergency summit of EU leaders to consider any UK request for further extension
- Friday, 12 April: Brexit day, if UK does not seek/EU does not grant further delay
- 23-26 May: European Parliamentary elections
If Mrs May wants to hold another vote on her Brexit deal in Parliament, it must comply with Commons Speaker John Bercow’s ruling that it can only be brought back with “substantial” changes.
That is why the government separated the withdrawal agreement from the political declaration – on the future relationship with the EU – for Friday’s vote.
The withdrawal agreement is the part of the Brexit deal Mrs May struck with Brussels which sets out how much money the UK must pay to the EU as a settlement, details of the transition period and the so-called Irish backstop arrangements.
Following Friday’s vote, Mrs May said there would be “grave” implications of rejecting the deal and warned they were “reaching the limits of this process in this House”.
Her comments led to speculation the PM could try to call a general election.
But Foreign Office minister Sir Alan Duncan told The Observer: “If we have a general election before Brexit is resolved, it will only make things worse.”
Under the terms of the Fixed Term Parliaments Act, the prime minister needs a two-thirds majority in order to call an election.