Brokenshire's promise of another vote two weeks later is created to discourage lawmakers from binding the government's hands this week.
Last month, Parliament voted in favour of an amendment that supported most of the PM's deal but called for backstop - which is a last-resort option to prevent a hard border in Ireland - to be replaced with "alternative arrangements".
May wrote Sunday to opposition Labour Party leader Jeremy Corbyn, with whom she has talked since her agreement was emphatically defeated in the House of Commons last month.
Opponents of the government accuse May of deliberately wasting time so that Parliament will face a last-minute choice between her deal and no deal.
'We can't allow that to happen, ' Sir Keir said.
After a meeting with the European Union Commission, Jean-Claude Juncker, alongside, President Donald Tusk, UK Prime Minister, Theresa May said on Thursday, the 7th of February, that, she had observed and heard, a yearning from the European Union leaders to ensure that Britain was not leaving without a practical deal.
"I think that gives that sense of timetable, clarity and goal on what we are doing with the European Union - taking that work forward and our determination to get a deal - but equally knowing that role that Parliament very firmly has". 'There needs to be a day when Parliament says that's it, enough is enough'.
However, Labour is facing its own deep splits on Brexit, with dozens of MPs furious with the leadership to failing to get behind a second referendum.
DIT says that with the agreement the British vehicle industry, which has consistently warned against a no-deal Brexit, could avoid up to £8m a year in tariff charges on their exports that would apply if the agreement had not been reached.
In a speech in Coventry he said Labour's plan "could win the support of Parliament and bring the country together" but Mrs May has so far "chosen the path of division". A similar motion will be tabled on Thursday if, as seems inevitable, May has not yet agreed enough changes to her overwhelmingly rejected departure plan to put it to another vote. Foremost was a demand that May seek a "permanent and comprehensive UK-wide customs union".
The UK has signed an agreement with Switzerland ensuring the trading relationship between the two nations will continue after Brexit, the British government said.