Boris Johnson’s controversial Brexit legislation enabling the UK to break international law has cleared a major Commons hurdle after MPs backed a Government compromise.

Tory backbench pressure forced the Prime Minister to agree to amend the United Kingdom Internal Market Bill in order to give MPs a vote before the Government can use powers which would breach the Brexit divorce deal brokered with Brussels last year.

Ministers have argued such powers to override the Withdrawal Agreement are needed to protect the relationship between Great Britain and Northern Ireland.

The Bill also sets out the way that trade within the UK will work once outside the EU’s single market and customs union, amid concerns in Westminster that Brussels could seek to disrupt food goods travelling from Britain to Northern Ireland as part of trade talks.

But the legislation did not originally contain a parliamentary “lock” on the use of the powers, prompting backbench uproar.

The compromise amendment was supported without the need for a formal vote on Tuesday.

Opponents among the Tory ranks still exist and have expressed concern about the prospect of the UK’s willingness to break international law.

Former prime minister Theresa May previously told the Commons she could not support the Bill as it will cause “untold damage” to the UK and threaten the future of the Union.

Mrs May launched a stinging rebuke of Mr Johnson’s actions, and said an arbitration process was already available to deal with disputes without the need for the new powers contained in the Bill.

Conservative former minister Sir Bob Neill, who led the backbench rebellion, told the Commons: “I commend this Bill now that the other little obstacle that might potentially have been in its way has, I hope, been resolved and I hope we can get on with the serious business of making what – to be frank from my point of view – is the best of a bad job.

“It’s not where I wanted to be, but in the interests of the country it’s right that we do get a proper functioning, working set of rules to enhance and improve the internal market within the UK.”

For Labour, shadow business minister Lucy Powell said the “legislative hooligans” in Number 10 had “won out” when the Bill could instead have achieved support.

She said: “Most, including the Labour Party, support the intention behind this Bill.

“An internal market Bill could have achieved widespread support. A strong, flourishing UK internal market respecting the devolution settlement and underpinning the union.

“Northern Ireland’s unique place within our union safeguarded, a successful trade deal with the EU delivered.

“Yet the legislative hooligans in Number 10 won out and instead we have this blunderbuss of a Bill fronted by the Prime Minister which undermines each and every one of these intentions.”

Business minister Paul Scully said: “This Bill will establish a market access commitment by enshrining mutual recognition and non-discrimination in law.

“The principle of mutual recognition is that goods and services from one part of the UK will continue to be recognised across the country.

“That ensures that the devolved administrations will benefit from freedom outside the EU.

“As the transition period ends, they’ll gain increased powers to set their own rules and standards across a wide range of policy areas within their competence.”

Earlier in the fourth and final day of the Bill’s committee stage debate, SDLP leader Colum Eastwood also said: “This Bill is unfixable, it’s probably unamendable, it is an assault on international law, an assault on devolution and it is, I think, the beginning of the biggest act of economic self-harm that we have seen in many a year.”

The Bill will return to the Commons next week to undergo further scrutiny.