Shadow Brexit Secretary Sir Keir Starmer [PA Wire] However, MPs are now set to be promised another vote if a new deal hasn't be struck by 27 February, where they will also be able to make suggestions - including extending the Article 50 deadline.
If no deal on the changes to the Brexit Withdrawal Agreement has been reached with Brussels by Wednesday, as seems overwhelmingly likely, Mrs May will address MPs on progress made, say more time is needed for negotiations, and table a "neutral motion" for debate the following day.
Labour is proposing its own Brexit plan, which would involve the United Kingdom staying in a customs union with the EU, which they say could get the backing of a majority of MPs.
The UK has signed an agreement with Switzerland ensuring the trading relationship between the two nations will continue after Brexit, the British government said.
"We can't allow that to happen", Sir Keir told The Sunday Times.
Labour wants to force the government to bring back a "meaningful vote" on Theresa May's Brexit deal by the end of this month.
"There needs to be a day when Parliament says that's it, enough is enough".
Mr Brokenshire refused to commit to this in an interview with the BBC's Andrew Marr Show, saying there could be more votes on amendments to the proposed deal instead.
"It's this blinkered approach that's got us to where we are, with her never wanting to see where the real majority is in parliament".
Christine Lagarde spoke at the World Government Summit in Dubai, where she didn't hesitate to criticize Britain's upcoming departure from the European Union, known as Brexit.
If no new deal has been reached with the European Union by Wednesday, May will make a statement to Parliament that day, and table a motion for debate Thursday.
May has been seeking changes to the deal with Brussels since it was rejected by a record majority in parliament on January 15. Question marks linger over the departure date as Theresa May still struggles to strike a negotiated deal that can win the backing of parliament.
The impasse has left the world's fifth largest economy facing an uncertain future, rattling financial markets and businesses about the prospect of a disorderly exit from the bloc that could damage the economy. While UK PM May's comment might appear to sooth an ongoing drama over Brussels, the European Union leaders had asked for insurance for Northern Irish borders, which appeared to be complicating the overall complexion of the recent round of talks.