Tuesday's Commons debate marked the start of the government's attempts to undo most of the changes to its EU Withdrawal Bill that were put forward by the House of Lords.
Conservative lawmaker Phillip Lee, who voted in Britain's 2016 referendum to remain in the European Union, resigned as a justice minister so he could vote against the government on a measure that would give Parliament more power over the terms of the break.
He said that remaining in the EEA, which includes membership of the single market, was not a ideal solution.
Earlier, May appeared to have also stemmed a rebellion over her commitment to leaving the EU's customs union which will transform Britain's trading relationships for decades to come.
One Tory Leaver said: "We need to know more about what exactly the prime minister has told the rebels".
They reassured anti-Brexit MPs that the government would accept some of their core demands to give parliament a meaningful say on the terms of Britain's European Union divorce, including - potentially - a new deadline for a deal to be agreed with Brussels that could make it hard for the government.
Davis warned lawmakers the government would never allow them to "reverse Brexit" and called on them to back its own amendment, which proposes a 28-day breathing space if parliament rejects a Brexit deal, during which the government would have to make a statement on its plans. And if there is still no agreement before February 15 parliament would vote on whether to take over the Brexit process.
Flint said she could not support EEA membership because it would mean there would be no restriction on free movement.
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In a day of drama, May's position seemed suddenly weaker when junior justice minister Phillip Lee, who has always been critical of the government's Brexit strategy, resigned and said he would vote against the government.
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 global treaties, and respecting the referendum result", a spokesperson for the Brexit department said in a statement.
As the vote approached, Tory MPs intending to defy the party whip in order to vote with Labour on the amendment left the chamber.
Prior to the vote, Labour's staunch pro-EU MPs - such as Chuka Umunna and Owen Smith - pleaded with the leadership to embrace the Norway option, as they believe it's the best chance retain full access to the single market.
Sarah Wollaston, a prominent Tory Remain rebel, has indicated that she will accept this pledge from the Government, and will therefore not be voting against her party.
But one minister told the BBC he would commit only to "further discussions". She now relies on the support of a small Northern Irish party.
Shadow Brexit Secretary Keir Starmer commented: "This vote was about ensuring parliament was given a proper role in the Brexit negotiations and that we avoid a no deal situation, which is becoming more likely with the divisions at the heart of this government".
"The decision was taken by the people, we gave them that decision and we have to stand by it", said Conservative MP Bill Cash.