"A meaningful vote is not the ability to reverse the decision of the referendum".
The Bill is now at the stage known as "ping pong".
"Labor will only vote for a final Brexit deal if it delivers a strong relationship with the single market based on full tariff-free access and ensures no loss of rights and standards", Labor leader Jeremy Corbyn said on Facebook.
"If, in the future, I am to look my children in the eye and honestly say that I did my best for them I can not, in all good conscience, support how our country's exit from the European Union looks set to be delivered".
She added she was sure Mrs May "will honour her word". It was a measure of the division in the party that out of 257 Labour MPs, 90 ignored that instruction and voted.
'Certainly it now seem inevitable that the people economy and culture of my own constituency will be affected negatively.
She added: "I can not countenance parliament being able to overturn the will of the British people".
Dr Lee also called for another national ballot on Brexit.
Theresa May is being told to stick to her promises by Tory Brexit rebels after Downing Street sowed confusion over what it had agreed in a last-ditch deal on key Brexit legislation.More news: Melania Trump's 'I really don't care' jacket causes a stir
"So it behoves us all to demonstrate discipline and unity of objective in support of the Prime Minister".
'So much classier to resign on principle when nobody is expecting it, than to threaten resignation but never follow through, ' he said.
One of the biggest changes to the Bill, and would have a dramatic impact on Brexit.
"We already know tens of millions, in fact hundreds of millions, have been invested by United Kingdom companies to create continuity post a worse-case Brexit scenario".
After PMQs, a No 10 source was asked if that meant, "as far as the government's concerned, clause C is not up for discussion as part of this amendment?"
Labour's Chuka Umunna, who backed staying in the European Union, welcomed the concession as the end of the government threatening to allow Britain to crash out of the European Union without a deal.
The government fears a weakened negotiating position.
Last night Mrs May delivered a direct warning to backbench Tory MPs that any defeats would encourage Brussels to turn the screw.
The amendment on the customs union probably has majority support in the House of Commons, but the clause is so loosely worded that the government doesn't consider it binding.More news: Obama Blasts Trump For 'Ripping Children From Their Parents' Arms'
The Prime Minister is now expected to get through the latest round of crunch Brexit votes unscathed, with a potentially explosive clash over the customs union on Wednesday already defused by a compromise amendment.
Flashpoints include proposals to increase the power of parliament to decide on the final Brexit deal, and others seeking to keep Britain tightly aligned with the EU's economy after it leaves the bloc.
Before the vote on the Labour amendment, which the party lost by 322 to 240, lawmaker Laura Smith resigned from her junior role in the team "shadowing" the cabinet office and five others left their roles as parliamentary private secretaries.
Meanwhile, Remain-backing Labour MPs made passionate arguments for Britain to stay in the EEA, telling the Commons it would save the economy from Brexit.
This amendment takes the power away from ministers to decide when law brought back from the European Union can be changed.
Mr Grieve said he hoped a compromise would be found and warned "this isn't the end of the matter" if that did not happen. "Not a single Conservative voted against it". I've made that quite clear'.
It would also give hard Brexiteers the chance to "scupper a good deal", she claimed.
But pro-EU Conservative lawmaker Dominic Grieve said that with the government's move "I am quite satisfied that we are going to get a meaningful vote on both "deal" and 'no deal"' scenarios. But if the Lords amendments are allowed to stand, that negotiating position will be undermined'.More news: Pepe Says Portugal 'Privileged' To Have Cristiano Ronaldo