Meanwhile, Tory backbenchers are threatening to bring down her government.
May has struggled to get backing for her plans to cut ties with the European Union, forced to find a compromise last week with pro-EU lawmakers in her Conservative Party to try to get their backing for her Brexit blueprint, or the European Union withdrawal bill.
In this spirit there were some classic exchanges in the Lords on Monday last night as rebellious peers comfortably pinged the Brexit Bill back into the Commons.
"Agreeing to amendable motions would allow parliament to direct the government on its approach to exiting the European Union, binding the prime minister's hands and making it harder to secure a good deal for the United Kingdom", he told reporters.
Mrs May insisted she was a woman of her word and had listened to rebels' concerns and acted on them.
Among the Tory peers who voted against the government were senior figures such as Michael Heseltine, Chris Patten and Sayeeda Warsi. The decision of the Lords represents another blow for May and the appeal will have to be discussed again on Wednesday in the House of Commons.
"What we have been seeking to do is improve a bill which has to go on the statute books", Conservative peer Patrick Cormack told his fellow Lords as he said he would be backing the amendment.
Brexit-backers oppose the amendment as they say it strips the government of negotiating leverage if it can't walk away, and they also think its proponents are trying to reverse the divorce.
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The government's current stance is that if MPs reject the Brexit deal, or if no deal has been agreed by 21 January 2019, parliament will be given the chance to vote on a "neutral motion" stating it has considered a minister's statement on the subject.
Grieve added: "One of the reasons I've supported [the amendment] is precisely to avoid the sort of crisis a government would immediately collapse".
Britain's house of lords has voted to allow lawmakers to decide on the fate of a final brexit deal.
"The meaningful vote is nothing to do with holding the government to account", Jacob Rees-Mogg, who leads a grouping of Anti-EU Conservative lawmakers, said after a speech in central London.
"We can not let Parliament tie the Government's hands", she said at an event in Omagh, Co Tyrone.
Hailsham said the government's offer not only failed to deliver a promised meaningful vote but was worse.
Asked whether he still trusted Theresa May, Mr Grieve said: "I am very conscious that the Prime Minister is in great difficulty".
May's Conservatives do not have a majority in the unelected House of Lords, and with the opposition Labour Party deciding to back a rival proposal, the government faces defeat when the debate begins on Monday afternoon.