Mr Grieve withdrew his own amendment, which would have given MPs powers to dictate what the Government should do if no acceptable agreement is reached by February 2019.
The Prime Minister avoided losing any of the 15 votes on amendments sent down from the Lords. Commons Leader Andrea Leadsom echoed Bercow, adding that "any threats of violence and intimidation are utterly unacceptable to the Government".
The Tanaiste Simon Coveney will brief the Cabinet today on the status of Brexit negotiations.
She won a succession of votes on Tuesday overturning Lords amendments, including one which would have removed the date of Brexit on March 29 2019 from the text of the Bill. But she faces a gruelling bout of "parliamentary ping-pong" with the Lords, as the Bill bounces back and forth in the coming weeks.
But these putative pledges by the PM are inconsistent with Tuesday night's statement by Davis's officials that any new amendment relating to the power of MPs to accept or reject a Brexit deal must not restrict her negotiating freedom - or restrict her ability to sign whatever treaty with the European Union she would like.
But Solicitor General Robert Buckland publicly implied that Government would be accepting part of Grieve's amendment, and said that a "structured discussion" would take place with rebels.
The Government has avoided a major defeat on its Brexit Bill after a last-minute concession, Tory rebel Dominic Grieve explains just exactly what the concession was.
Theresa May has suffered a ministerial resignation ahead of crunch Commons votes on Brexit, with Phillip Lee hitting out at the Government's "irresponsible" approach.
Anthony Bourdain’s ex shares photo of their ‘strong’ 11-year-old daughter
Ottavia Busia posted the photo of Ariane , 11, on Instagram with the caption: "Our little girl had her concert today ". Ariane has been performing live in front of crowds since a year ago, according to posts from Ottavia.
They believe that if there is no Brexit deal by the end of November, the government must clear its next course of action with MPs.
I have to say I do feel a bit uneasy about what deal they have got because they seem very pleased with themselves.
The government was putting a combative spin on the concessions Tuesday evening: "The Brexit Secretary has set out three tests that any new amendment has to meet - not undermining the negotiations, not changing the constitutional role of Parliament and Government in negotiating worldwide treaties, and respecting the referendum result", a spokesperson for the Brexit department said in a statement. He said: "Facing the prospect of a humiliating defeat, Theresa May has been forced to enter negotiations with her backbenchers and offer a so-called concession".
"We will put in front of Parliament the decision for them to vote. after that there will be a process of primary legislation to put the actual details of it in Parliament, so Parliament will actually decide on the application of the detail".
Pro-Brexit tabloid the Sun warned lawmakers on Tuesday's front page that they had a choice: "Great Britain or great betrayal".
"Time will tell as to whether this is just another attempt to buy off the rebels or a real attempt at consensus".
"Here we are on the eve of an important June summit. and we've no landing zone".