A total of 89 of the party's 257 MPs ignored front bench orders to abstain from voting either for or against the EEA amendment.
Grieve told media in London the new version was unacceptable because wording made it impossible for MPs to change the government's proposals. "I hope they listen to me when I say I don't understand why you've done this last-minute switch", he added.
Asked if the prime minister's words ruled out a discussion on the contentious rebel clause, her spokesman said: "I think that is a fair assessment".
"At the end of the process something was inexplicably changed, which had not been agreed", Mr Grieve is quoted as saying. It will provide a functioning statute book on the day we leave the European Union, as well as ensuring that it is for our sovereign Parliament to make any future changes.
She convinced Tory Remainers not to go ahead with a bid to bolster the "meaningful vote" on Tuesday by telling them she would find a compromise way forward.
The issue with Grieve's position identified by Brexiteers is that it effectively allows Remainer MPs to reject any deal the Prime Minister produces as "not good enough" and to reject the alternative of "No Deal" as well - effectively cancelling Brexit.
Last night Tory Remainers resubmitted their original amendment to the Lords, where it will be debated along with the government amendment.
Mrs May avoided nearly certain defeat in the House of Commons on Tuesday by inviting potential rebels into her private office and assuring them that their concerns about having a "meaningful vote" on the final Brexit deal would be addressed.
The poll saw the biggest swing - 19% - from a Labour opposition to the pro-EU Lib Dems since 1983.
"Grateful for the conversations but without consultation what was agreed earlier today has been changed", she said.
Sarah Wollaston, who is also unhappy with the current state of the government's flagship Brexit bill, claimed a compromise agreed with ministers had "acquired a sneaky sting in the tail" by the time it was formally tabled.
"Would be amusing if only it wasn't such a serious issue, Preventing the most destructive Brexit matters to the majority in Parliament..."
Crucially, the motion will be unamendable, meaning that MPs can not insert a requirement for Mrs May to go back to the negotiating table, extend the Brexit transition or revoke the UK's withdrawal under Article 50. Commenting on the proposal, shadow Brexit secretary, Kier Starmer, said the Lords amendment suggests helpful developments in policy, including proposals to enable the watchdog to initiate legal proceedings. After this happens, pro-EU members of her party will likely push for a vote in the House of Commons. "Parliament can not - and should not - accept it".
Jeff Smith is yet to comment but speaking ahead of the vote, Labour leader Jeremy Corbyn said: "The Labour party respects the outcome of the European Union referendum and does not support the EEA or Norway model as it is not the right for option for Britain".
The prime minister narrowly avoided a damaging defeat this week when she bought off rebel MPs with a promise of more control over negotiations.
As with David Davis' constant resignation threats, there is a risk the rebels will turn into the boy who cried wolf - they have threatened again and again to make life hard for her, before capitulating on every vote.
Mr Hill said: "I voted to support my constituents on the Brexit Bill".
Eight injured after taxi ploughs into fans in Moscow
Russian authorities have promised to host a safe World Cup tournament, which is taking place in 11 cities until 15 July. Preliminary information indicated that the driver, who had a Kyrgyzstani driving license, lost control of the vehicle.