The Prime Minister offered MPs new assurances that Parliament will be able to exercise control over the controversial European Union "backstop" if they back her Brexit deal in a crunch vote next week.
"We're discussing with Downing Street what these clarifications might amount to".
Nevertheless the vote will be seen as another blow to Mrs May's authority as she struggles to win support for her Withdrawal Agreement. Mr Roache said he was glad the PM had "finally picked up the phone" but that her deal was not "good enough".
MPs are due to vote on her withdrawal agreement on Tuesday night, but it is widely anticipated that it will be defeated, with backbench Brexiteers and the DUP vehemently opposed to both the Northern Irish backstop clause and the £39bn divorce bill.
The Government would remain under an worldwide obligation to keep the border open, and it is understood ministers would be expected to seek alternative arrangements, possibly involving the use of new technology, within the 12-month deadline.
An analysis by the BBC on Thursday suggested May's deal is on course to suffer the biggest government defeat in the history of the Commons in the vote on January 15.
The amendment put forward Wednesday by Grieve was supported by former Tory ministers Sir Oliver Letwin, Jo Johnson (the brother of hard Brexiteer and former Foreign Minister Boris Johnson) Guto Bebb and Sam Gyimah.
She would then have a further seven days to put a motion to the House of Commons, which MPs could amend to try to direct the government's strategy.
May told parliament on Wednesday that the only way to avoid a no-deal Brexit is to vote for the deal.
Mr Hunt warned that failure to deliver Brexit would be "incredibly damaging" for the United Kingdom and something the country would regret for "many, many generations".More news: Health officials: 13 Oklahomans have died from the flu
"That is what I have tried to do and what I will go on doing".
The amendment passed through the House of Commons 308-297 and was submitted by Dominic Grieve, the Tory MP and former attorney general.
Labour front bencher Barry Gardiner told the BBC Today programme yesterday morning that "it is expected that the government next Tuesday will be defeated on the most important piece of legislation that has come before Parliament in 50 or more years..."
Asked whether she agreed with Mr Hunt that the United Kingdom can thrive after a no-deal Brexit, Ms Rudd told Today: "This is a strong and great country, we will find a way to succeed, but I do not think that no deal would be good for this country and I'm committed to making sure we find an alternative".
Crispin Blunt was among those to question the Speaker's impartiality, saying many will have the "unshakeable conviction that the referee is no longer neutral".
It is expected that Juncker and European council president Donald Tusk will issue a letter to May on Monday in a last ditch bid to convince MPs to back the deal.
"Moving into office at a period right up against the clock, there would need to be time for that negotiation", Corbyn said.
Mr Bercow said he was acting in the interests of MPs and had made an "honest judgement".
"I just invite you to reflect on the conclusion that many of us will have inevitably have come to". Andrea Leadsom, the leader of the House of Commons, said Bercow should publish the advice he received from the Commons clerk, Sir David Natzler.
She repeated that resolve during a noisy Prime Minister's Question Time in the House of Commons, telling the main opposition leader, Labour's Jeremy Corbyn, and other MPs that the best way to avert a no-deal Brexit was to vote for her deal.