The European Union (Withdrawal) Bill, or "Repeal Bill" as it has been dubbed by the government, provides for the repeal of the 1972 European Communities Act, which gives recognition to the superiority of EU law in the UK.
Their claim was that the European Union withdrawal bill handed sweeping powers to government ministers that would allow them to by-pass the elected parliament.
The matter divided Cumbria's MPs with three voting in support of the bill and three against. They would back the bill if it had amendments, which is what Labour suggested in the beginning.
The Government says the bill is essential to put the result of last year's referendum into effect, and Theresa May hailed the passage as a "historic decision".
"It is purely procedural".
The "EU Withdrawal Bill" would end the supremacy of EU law in the UK.
Tory Brexiteer Peter Bone (Wellingborough) said: "I notice this particular programme motion is one of the better ones because it's eight days long and has eight hours protected time".
"The goal of this is to give certainty over our laws from the start".
The vote was passed by a comfortable majority of 36 - which included all 10 of the DUP MPs that are propping up the minority government.
Those tabled by Labour include plans to strip out the bulk of the Henry VIII powers, including deleting a clause which lets ministers amend any legislation affected by Brexit by decree.
These amendments are backed by normally loyal Tory MPs, such as John Penrose, Vicky Ford and Tom Tugendhat. Jeremy Corbyn has called this present bill a "power grab" and it is understandable why he thinks this.
Conservative MPs warned Prime Minister Theresa May that support for her latest Brexit legislation was by no means unconditional, demanding extensive changes to the bill on withdrawal from the European Union just minutes after backing it in Parliament.
"Just look at the mess they've made of the opening negotiations".
The vote Monday was on the second reading of the bill, when lawmakers are asked to vote on the general principle, rather details.
This was in response to a Department for Exiting the EU (DExEU) paper due to be released on Tuesday which says Britain would continue to contribute to EU defence operations after it completes its divorce in March 2019.
These laws can be changed or deleted by MPs after this date.
Much of the media focused on a rebellion among Labour MPs, seven of whom defied a three-line whip to back the Bill, with a further 13 abstaining.