The Lib Dems said the "so-called Tory rebels" had "lost their bottle and caved into yet another pathetic government compromise that isn't worth the paper it is written on", while SNP leader Nicola Sturgeon said the concession was a "fudge".
"And in the circumstances that might follow a no deal, which would undoubtedly be one of the biggest political crises in modern British history, if the house wishes to speak ... the house has the power to do it", Grieve said.
As reported, the government bill on the conditions for Britain's withdrawal from the European Union went through parliament despite the resistance of some of the deputies of the ruling Conservative Party.
Appalling mixed metaphors aside, most of the proceedings was taken up with very tiresome perorations in the House on Brexit as national disaster, catastrophe and apocalypse all rolled into one.
The EU 's chief negotiator Michel Barnier said on Tuesday that "serious divergences" remain over how to avoid border checks between Northern Ireland, a part of the United Kingdom, and neighbouring EU member Ireland. Relationships between MPs had been "strained nearly beyond belief", she said.
"The vote will be tight", a government source told AFP.
After pro-EU Conservative lawmaker Dominic Grieve said he would support the government's proposal for a "meaningful vote" in parliament on any Brexit deal, a potential rebellion that could have undermined May's authority looked was averted.
However, the government has chose to suspend this tradition for the crunch vote on the "meaningful vote" amendment, meaning ill MPs must overcome their sickness to physically take part in the vote.
On Wednesday evening, following the Commons vote, Leader of the Lords Baroness Evans of Bowes Park said the EU (Withdrawal) Bill had been "debated at length" and was very different as a result of amendments tabled by the Lords.
"I believe our role now is to accept their view as expressed in a vote a few hours ago", she said.
In other words, come November, the Government could plough ahead with no deal regardless even if MPs voted to urge it to renegotiate.
MPs will then vote on this statement.
"If the motion is not in neutral terms it doesn't meet the requirement of the Act of Parliament".
Flagship legislation returns to the Commons after the Lords again backed giving MPs a "meaningful" say on the final deal.
Grieve told the House of Commons he now saw the need to take account of May's concerns over the state of the negotiations.
Mr Davis's statement also mentioned MPs being able to table their own motions and have votes on them. Other rebels have also reportedly, "called off the revolt", including former cabinet minister Nicky Morgan.