MPs voted 295 to 221, majority 74, to give the Northern Ireland Protocol Bill a second reading, which clears the way for it to undergo detailed scrutiny in the coming weeks.
The Prime Minister claimed the proposed legislation, which gives ministers powers to override parts of the post-Brexit deal on Northern Ireland, could be carried out “fairly rapidly”, with the proposals in law by the end of the year.
But his predecessor in No 10, Theresa May, led the criticism from the Tory benches as she delivered a withering assessment of the legality and impact of the Bill.
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Mrs May made clear she would not support the legislation and warned it will “diminish” the UK’s global standing.
Other Tory MPs joined Mrs May in expressing concern, although they opted against seeking to block the Bill at second reading and instead appear likely to seek amendments.
The House of Lords is also expected to contest parts of the Bill, setting up a lengthy showdown between the two Houses.
Mr Johnson’s Government has said the measures to remove checks on goods and animal and plant products travelling from Great Britain to Northern Ireland are necessary to safeguard the Good Friday Agreement and peace and stability.
“What we are trying to do is fix something that I think is very important to our country, which is the balance of the Belfast/Good Friday Agreement,” he told reporters at the G7 summit in Germany.
“You have got one tradition, one community, that feels that things really aren’t working in a way that they like or understand, you’ve got unnecessary barriers to trade between Great Britain and Northern Ireland.
“All we are saying is you can get rid of those whilst not in any way endangering the EU single market.”
Asked if the measures could be in place this year, Mr Johnson said: “Yes, I think we could do it very fast, Parliament willing.”
He said it would be “even better” if we could “get some of that flexibility we need in our conversations with Maros Sefcovic”, the European Commission vice-president.
The Prime Minister added: “We remain optimistic.”
Foreign Secretary Liz Truss attempted to downplay concerns of MPs by saying the Bill has a “strong legal justification” and the UK remains committed to seeking a negotiated solution.
But Mrs May told the Commons: “The UK’s standing in the world, our ability to convene and encourage others in the defence of our shared values, depends on the respect others have for us as a country, a country that keeps its word, and displays those shared values in its actions.
“As a patriot, I would not want to do anything that would diminish this country in the eyes of the world.
“I have to say to the Government, this Bill is not, in my view, legal in international law, it will not achieve its aims, and it will diminish the standing of the United Kingdom in the eyes of the world, and I cannot support it.”
Conservative former Northern Ireland secretary Julian Smith also said: “I fear that this Bill is a kind of displacement activity from the core task of doing whatever we can to negotiate a better protocol deal for Northern Ireland.
“I also fear that it risks creating an impression to unionism that a black-and-white solution is available, when the reality is once this Bill has been dragged through the Lords, and courts, and EU responses and reprisals, compromise will ultimately be needed.”
But Conservative former justice secretary Sir Robert Buckland said there is necessity for the Government to act because there is a growing and “real threat”.
Unionist opposition to the imposition of checks has seen the Democratic Unionist Party (DUP) refuse to return to the powersharing Executive at Stormont, leaving the region without a functioning government.
DUP leader Sir Jeffrey Donaldson acknowledged the Bill is not perfect but said: “It empowers ministers to make change where change is necessary to ensure the proper functioning of the UK internal market.”
Sir Jeffrey, ahead of the debate, also warned the Lords that blocking the legislation would be akin to “wrecking the Good Friday Agreement”.
Alliance MP Stephen Farry (North Down) said: “This is an extremely bad Bill, it’s unwanted, unnecessary and, indeed, it’s dangerous.”
Sinn Fein MP John Finucane called the Government’s plans “shameful” and said they will mean “more instability” for the region.
He told BBC Radio Ulster’s Good Morning Ulster programme: “It’s very interesting that we are watching a sovereign Parliament debating whether to continue a breach of international law or not.”
A Number 10 spokesman said on Monday that the Government had never put a “hard target date” on when it would hope to see the Bill enacted.