But in a separate blow for the PM, she was defeated on an amendment which calls for the United Kingdom to stay in the European medicines regulatory network, losing by 305 to 301.
Theresa May came within six votes of the possible collapse of her government as MPs narrowly rejected an amendment to trade legislation that could have forced the United Kingdom to stay in the EU customs union.
The amendment from former minister Stephen Hammond would have forced the United Kingdom to default to membership of the EU's customs union if it proved unable to negotiate a better agreement by January 21 of next year.
The Prime Minister was saved from a humiliating reverse by the votes of four Labour Brexiteers - and one now sitting as an independent - who backed the Government in the crucial division.
This article has been adapted from its original source.
On Monday evening, a vote on another amendment was even closer, with the government winning by just 3 votes (305 votes to 302).
Of course the white paper was released prior to the amendments to UK Brexit legislation that will dictate its approach to trade and customs negotiations, therefore the white paper that Barnier struck a relatively constructive tone on has changed, and most likely changed for the worse in Barnier's view.
According to the Daily Telegraph, the party's "Eurosceptics have set up a "party within a party" with a highly organised whipping operation among Tory Eurosceptic MPs to try to frustrate Theresa May's Brexit plans".
But the Government did not move the motion amid growing Tory opposition to the plan, with several Conservative MPs having indicated they would vote against any attempt to cut short the term with so much work to do on Brexit.
While critics have said accepting the changes to the legislation mean the prime minister's recently announced Chequers deal was "dead in the water", Mrs May insisted this was "absolutely wrong" and that the changes were "consistent" with her plan.
No fast track capacity to create a new customs union.
Later in the day, May lost another, less symbolic, parliamentary vote called by pro-Europeans to ensure that British pharmaceutical companies would be regulated by the European Medicines Agency. She was saved by Labour eurosceptic MPs.
The British government wants to retain the ability to sign trade deals independently of the EU.
The Electoral Commission said the "Vote Leave" group, backed by senior politicians including former foreign secretary Boris Johnson, failed to declare 675,000 pounds ($894,000) it spent with Canadian data firm Aggregate IQ.
If parliament does finish for summer earlier than expected, there will not be enough time for Tory MPs to hold a no confidence vote against the PM.
"Bullish comments by Bank of England speakers will drive the GBP higher, only to be depressed once Brexit headlines hit", says Terence Wu, a treasury analyst with OCBC in Singapore reflecting the sense markets that until Brexit headlines improve, Sterling will ultimately struggle. He said the slender margin by which the vote was passed showed how important it was to continue to fight for a clean Brexit.