Mr Sunak had initially failed to guarantee that MPs would be offered a binding vote on the matter and said they would instead be offered an opportunity to “express their view” in Parliament, sparking fury from grumbling backbenchers.
However, he confirmed on Monday that MPs will be offered a formal vote on the new deal in the coming weeks. The Prime Minister told reporters: “Yes, Parliament will have a vote at the appropriate time and that vote will be respected.”
It is thought that a vote on the fresh Brexit deal could come later this month, and potentially after the Budget on 15 March, with Mr Sunak saying MPs would require some time “to digest” the complex new legislation.
The Prime Minister added: “It is important that we give everyone the time and the space they need to consider the detail of the framework that we have announced because it is comprehensive in nature.”
Mr Sunak unveiled his new Windsor Framework earlier this week, which is designed to fix problems with the Northern Ireland Protocol.
Under the new legislation, which was co-signed by the Prime Minister and Ursula von der Leyen, the President of the European Commission, some EU-imposed checks on goods heading west over the Irish Sea will be eradicated.
As part of the deal, the EU will still have some power over Northern Ireland. EU law will still apply to some industries, particularly on food and animal products, and the European Court of Justice will remain the arbiter of how it operates.
However, the Prime Minister secured the so-called “Stormont Brake”, which will allow the Northern Ireland Assembly a veto to stop any new EU legislation applying in the region.
Mr Sunak has so far received broad support for the new framework, with Labour vowing to back the agreement.
However, the Prime Minister will still face hurdles getting the legislation through Parliament, with both the Democratic Unionist Party (DUP) and the European Research Group (ERG) of Tory MPs complaining that the EU has too much power over Northern Ireland.
The ERG said earlier this week that it will wait for a fortnight before delivering its verdict on the deal, and has resurrected its so-called “star chamber” of lawyers to pore through the detail of the agreement.
Mr Sunak hinted on Tuesday that he will press ahead with the deal even if the DUP rejects it. Asked if the deal would be “imposed” on the party against its wishes, Mr Sunak said: “This is not necessarily about me or any one political party. This is about what is best for the people and communities and businesses of Northern Ireland.”
Mr Sunak has been clear that he will give the DUP and eurosceptic MPs in the ERG time to consider the deal before holding any vote on the plans in the Commons.
However, the Prime Minister could face further headaches still, after Boris Johnson signalled last night that he is ready to join a Commons rebellion against Mr Sunak’s new Windsor Framework.
Speaking at the Global Soft Power Summit in central London, the former prime minister claimed the deal still leaves Northern Ireland subject to EU law and warned he will find it “very difficult” to vote for Mr Sunak’s new Brexit agreement.
“I’m conscious that I’m not going to be thanked for saying this, but we must be clear about what’s going on here,” he said.
“Although there are easements, this is really a version of the solution that was being offered last year to Liz Truss when she was foreign secretary. This is the EU graciously unbending to allow us to do what we want in our own country, not by our laws, but by theirs.”
It was expected that Mr Johnson would announce his opposition to certain details contained within the new agreement, but it remains unclear whether he will lead a fully-mounted rebellion against the framework in any vote on the matter.
The Government is understood to be confident that it has the support to get the fresh Brexit deal over the line with or without the support of rebels, with the number of MPs expected to voice their opposition to the plans thought to be as low as 20.