A total of 89 Labour MPs defied Corbyn in the vote on this amendment, making it the party's biggest Brexit rebellion yet.
But the Labour party announced five junior ministers had resigned ahead to the vote on EEA membership, signalling the group planned to rebel against the party line and back calls to remain in the institution.
Many MPs were frustrated at the front bench attempt to fudge away party differences.
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.
This ministerial resignation could be a one day drama, he could be replaced with little fuss. "And the closer we get to October, the less inviting the cold sea appears".
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.
The MP - who represents the Leave-voting area Crewe and Nantwich - was followed by Ged Killen, Ellie Reeves, Tonia Antoniazzi and Anna McMorrin.
Labour MPs had been whipped to abstain on the motion to disagree with the Lords EEA amendment. A week ago reports of as many as 120 were being touted. r.
This evening, I have resigned as Shadow Defence PPS to vote in favour of the Lords EEA amendment.
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Dismissing the Government's compromise, she tweeted: "Merely issuing a statement in response would make it a meaningless final vote".
John McDonnell, anticipating the revolt, admitted in a speech on Wednesday morning that the party was on a tightrope.
Perhaps the most significant compromise from Mrs May was on what happens if there's no deal. The free movement of people also applies in the zone as it does in the EU.
"The people, economy and culture of my constituency will be affected negatively" by Britain's European Union departure and it is "irresponsible to proceed as we are", Lee said.
"But also they want us to answer the question why hasn't Britain got the workforce it needs, why has social mobility stopped, why do we train fewer doctors than Holland or Ireland and why are these jobs dominated by those in the middle and upper classes so my constituents don't get a look in?"
Following a meeting with Theresa May, Tory MPs said they had been promised "input" into what the government would do if the United Kingdom faced a no-deal scenario.
Dr Lee added: "If Brexit is worth doing, then it is certainly worth doing well; regardless of how long that takes". May's preferred approach is temporarily keeping the U.K.in some form of temporary customs union with the E.U., but this is unacceptable to hardline Brexiteers in her party.
Cooper and Benn had introduced an amendment calling for EEA "with safeguards".
With not all rebels persuaded that May's plan can prevent an economic shock after Brexit, some say they will challenge her plans to leave the customs union again during votes on other bills, on trade and customs, which will be brought back to the house some time before July 24.