One of the amendments voted through by the House of Lords would force the Government to give MPs a "meaningful vote" on the final Brexit deal before the country withdrew from the bloc.
DAVID DAVIS has urged MPs to reject a Lords amendment on giving Parliament a vote on the final Brexit deal tonight as he says it could give Remainers a chance to KEEP us in the EU.
"As I said when moving to a vote, it gives the government time and space to think again".
Once it is agreed, the bill will go for Royal Assent by Queen Elizabeth II, after which it becomes law.
"Last year, we concluded that the previous government's decision not to instruct key departments to plan for a Leave vote in the European Union referendum amounted to gross negligence".
The Prime Minister's European counterparts had been prepared for her to make an announcement this week, with April 6 pencilled in as the date for a meeting of the 27 other EU leaders to respond to the situation - a gathering which will now be pushed back until later that month.
But Mr Grieve refused to vote with the Government, telling Mr Davis: "Somebody's got to put down a marker that we have to follow proper process in the way in which we carry out Brexit".
The upper house reviews and amends bills from the lower house.
The EU Withdrawal Bill could complete its final stages if both Houses of Parliament agree the text of the bill.
Peers are expected to back down in the face of opposition from the elected House, but some staunchly pro-EU members of the Lords could try to hold out.
Hannah White, director of research at the Institute for Government, highlighted the government's slim majority in the Commons. Commons can override Lords and given its earlier vote it may do just that, perhaps on Monday.
Labour sources warned there was a 20 per cent chance of peers sending the Bill back if their amendments were dismissed out of hand.
BBC chief political correspondent Vicki Young said she thought it likely that MPs would overturn the Lords' amendments to the bill, and did not expect the Lords to try to block the bill any further.
The source told Sky News that, this time, the Lords are nearly certain to vote it through unamended.
However, the government never had any intention of triggering Article 50 before the last week of March, a Number 10 spokeswoman said Monday.
Speaking on Sunday both David Davis and Liam Fox, two of Britain's most senior Brexit ministers, admitted that the United Kingdom was preparing for a scenario where it exited with no deal with the rest of the European Union - an eventuality that would see it forced to trade on World Trade Organisation terms.
'I've spent my whole career doing deals, negotiating with partners and getting results.