The government has won support in parliament for part of its new Brexit deal by 515 votes to 29, despite a rebellion from some of its own MPs and a backlash from members of the Democratic Unionist Party (DUP).

Northern Ireland Secretary Chris Heaton-Harris said the Stormont brake was “one of the most significant changes” in the post-Brexit plan for the region – “a robust change that gives the UK a veto over dynamic alignment with EU rules”.

But former prime ministers Boris Johnson and Liz Truss refused to back the policy, with Mr Johnson saying it would mean the “whole of the UK” was unable “properly to diverge and take advantage of Brexit”.

And DUP leader Sir Jeffrey Donaldson said he cannot commit his party “will restore the political institutions” in Northern Ireland as a result of the deal.

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Priti Patel, Jacob Rees-Mogg and Sir Jake Berry were also among the other high profile names to against the measure – a total of 22 Tories, six DUP MPs and one independent.

But hundreds more from across the Commons, including 280 Conservatives, backed the government’s plan.

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Rishi Sunak reached the new Brexit agreement, known as the Windsor Framework, in February with the European Commission in an attempt to fix ongoing issues with the Northern Ireland Protocol.

Unionists have been refusing to form a government in the region while the protocol is in place, saying it had created trade barriers in the Irish Sea and threatened Northern Ireland’s place in the UK’s internal market.

The prime minister said his plan, including new trade lanes, the reduction in EU laws, and the so-called Stormont brake – to stop changes to or new laws being brought in from the EU – offered a better future for Northern Ireland post-Brexit.

But the measures have not won over pro-Brexit Tories who form the European Research Group (ERG) or the DUP, who believe the EU will still have too much of a say over what happens in Northern Ireland.

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0:30

Mark Francois says the Stormont brake – a key feature of the new agreement that aimed to resolve issues with the Northern Ireland Protocol – is ‘practically useless’

Mr Sunak promised to give MPs a say on the plan in the Commons – and today they were given a vote specifically on the Stormont brake – the result of which would be seen by Number 10 as approving the whole deal.

A number of Conservative politicians gave the plan their support, with former Northern Ireland secretary Julian Smith saying the framework had made “huge strides”.

He pointed to polls in the region that showed the majority of Northern Ireland voters backed the plan, adding: “We must cherish, nurture and expand that support and consent at every opportunity.”

Conservative former minister Vicky Ford, who grew up in Northern Ireland, echoed his point, adding: “The people of Northern Ireland, and indeed the people in the UK, need to move on.”

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0:37

Steve Baker says he believes both Liz Truss and Boris Johnson ought to be voting for the deal

But Tory former minister Sir John Redwood said: “What is the point of rushing through a vote on this protocol when it is the protocol and the agreement behind it that prevents Stormont meeting, which means the protocol would never be used?”

The new agreement got the backing of Labour, with shadow Northern Ireland secretary Peter Kyle saying: “My party will be voting in unanimity today. It is [the Conservative] party that is getting in the way of getting this across the line, because it is [their] party that is split over how to vote on the issue before today.

“We are acting in the national interest. They are riven with division.”

The Liberal Democrats also gave their support. Speaking afterwards, MP Layla Moran said: “Conservative MPs are like mutinous pirates who no longer care what their captain says. After today’s latest debacle, it is time they abandoned ship and made way for serious politicians.”

However, DUP MP Jim Shannon also believed the framework was being “shoved” through, and saw the UK giving the EU “sovereignty over the courts and power over Northern Ireland”.

He added: “It… is being shoved through the House by the government – the Conservative and Unionist Party. With some dismay I actually question now, Conservative, and where is the unionist?”

Sir Jeffrey said his party would continue to “work intensively to solve these issues… in the knowledge that what has already been achieved has been because we were not prepared to accept the undermining of Northern Ireland’s place within the union of the United Kingdom”.