Johnson won the so-called second reading parliamentary vote on the Internal Market Bill 340 to 263.
"We cannot have a situation where the very boundaries of our country could be dictated by a foreign power or worldwide organisation", he said.
Speaking in the House of Commons on Monday evening, Johnson said the bill was "a package of protective powers" that was "essential to guaranteeing the integrity and sovereignty of the UK" and pinned the blame for needing it on the EU's "extreme" approach and "lack of common sense".
Sajid Javid, Conservative MP and the previous Chancellor of the Exchequer (finance minister, in other words), had also come out against the bill, saying in a tweet that he could not see why it would be necessary to break worldwide law in the instance of the Internal Market Bill.
He said Brussels negotiators were threatening to ban the sale of United Kingdom agri-food products anywhere in the European Union, creating an "instant and automatic" prohibition on the movement of such goods from Great Britain to Northern Ireland.
Johnson says the UK Internal Market Bill will ensure "unfettered access" for future trade within the UK's four nations - Scotland, England, Wales and Northern Ireland.
Johnson put forward the bill in Monday's debate with the claim that the EU was trying to force the United Kingdom to accept certain regulations and that the European bloc had threatened to use "an extreme interpretation" of the withdrawal agreement in order to do so.
All five of Britain's living former prime ministers have expressed concern about his plan.
"I understand how some people will feel unease over the use of these powers and I share that sentiment myself", Johnson said.
Cox, previously a strong supporter of Johnson on Brexit, said he wouldn't support the proposal when the House of Commons takes its first vote on the contentious legislation later Monday.
But senior Conservative MPs lined up to warn they could not back the plans after a minister admitted last week that they could breach worldwide law.
The EU has demanded Britain scrap the main parts of the bill by the end of September and that if not, there will be no trade deal at the end of the year to cover everything from vehicle parts to food. Both sides accepted the compromise to protect the open border, which helps underpin the peace process in Northern Ireland.
The row threatens to disrupt already tough post-Brexit trade negotiations, fuelling growing fears of failure that would see more than four decades of EU-UK integration come to a crashing halt at the end of this year.
Ed Miliband stood in for Labour leader Sir Keir Starmer who is self-isolating after a member of his family developed Covid symptoms.
A number of Conservative former ministers made clear that they would not support any measure which breached global law, including Andrew Mitchell, Sir Oliver Heald and another former attorney general Jeremy Wright. I'll very happily give way to him.