Signs of unity on sovereignty raise prospect of London mayor joining campaign to keep Britain in a reformed EU

David Cameron is moving towards signing up Boris Johnson to his campaign to keep Britain in a reformed EU after signalling that he is prepared to accede to the London mayor’s demand to assert the sovereignty of parliament.

The prime minister told Johnson in the House of Commons that he would introduce measures to “put beyond doubt” the sovereignty of parliament, in a move that was welcomed in private by the London mayor.

The signs of a rapprochement between the Eton and Oxford contemporaries came less than 24 hours after Theresa May had indicated that she may also be prepared to campaign to keep Britain in the EU. The home secretary described the proposals, tabled by the European council president Donald Tusk on Tuesday, as the “basis for a deal”.

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May and Johnson, who are both members of the political cabinet, were seen as the most senior Tory waverers who could have been tempted to campaign for a British exit from the EU.

Tory Eurosceptics had thought that momentum was swinging their way after the prime minister came under fire from the rightwing press and some wavering Tories for failing to deliver on his manifesto commitments. But with Johnson moving towards Cameron, out campaigners are now expected to only win the support of five less senior cabinet ministers led by the former party leader Iain Duncan Smith.

In a Commons debate on Britain’s proposed EU renegotiation, Johnson intervened to ask Cameron to explain how his EU reforms would “assert the sovereignty of this House of Commons and these Houses of Parliament”.

In response, Cameron told Johnson: “I am keen to do even more to put it beyond doubt that this House of Commons is sovereign. We will look to do that at the same time as concluding these negotiations.”

In his statement to MPs the prime minister signalled his support for a referendum on 23 June, after Jeremy Corbyn called on him to hold the vote on that date.

The Labour leader said that his party would campaign to keep Britain in the EU. But he was highly critical of the prime minister’s negotiations, which he described as a “Tory party drama” that could lead to a bonfire of workers’ rights.

Corbyn said: “In truth – in reality – this negotiation is a Tory party drama that is being played out in front of us, as we see at the moment … We believe that the prime minister has been negotiating the wrong goals in the wrong way for the wrong reasons.

“For all the sound and fury, the prime minister has ended up exactly where he knew he would be: making the case to remain in Europe, which was what he always intended, despite a renegotiation spectacle choreographed for television cameras over the whole continent.

“As his own backbenchers keep telling us, the proposals from the European council are simply tinkering around the edges. They have little impact on what the EU delivers for workers in Britain or British businesses.”

A few hours later, after the exchanges in the House of Commons, it became clear that the prime minister is prepared to deal with Johnson’s concerns on two levels. The prime minister is expected to:

Declare that the UK supreme court or another official body should be vested with powers akin to those of the German constitutional court, which has the right to assess whether legal acts by the EU’s institutions remain within the scope of the powers of the EU. Cameron first floated this idea in a speech at Chatham House in November after Johnson had outlined in a private plea to the prime minister to his calls for an assertion of parliamentary sovereignty.

Propose a possible fresh act of parliament to make clear that the UK’s agreement to the primacy of EU law – which dates back to 1972 – was gifted by parliament and could therefore be withdrawn by parliament.

The concessions to Johnson, delivered outside the prime minister’s formal EU negotiations, will be unveiled at the same time as the conclusion of the talks with Europe’s member states.

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Oliver Letwin, the prime minister’s policy chief, has been charged with drawing up the concessions in a way that will reassure EU leaders that Downing Street is not seeking to subvert the formal negotiations.

The signs that all the cabinet heavyweights will support the prime minister came as Eurosceptics made clear their deep unhappiness with the proposals tabled by Tusk. His main offering was an emergency that would allow the UK to limit in-work benefits to EU migrants for four years. The Eurosceptics said the proposal was riddled with flaws because other EU member states will be able to block it and the UK will have to start paying benefits gradually over the four years.

Jacob Rees-Mogg, the Tory MP for North East Somerset, told the prime minister: “The thin gruel has been further watered down. [The prime minister] has a fortnight, I think, in which to salvage his reputation as a negotiator.”

Downing Street received a more positive reception in the European parliament in Strasbourg, where MEPs embarked on an initial debate on the reform package. Jean-Claude Juncker, the president of the European commission, told MEPs that the Tusk proposals amounted to a fair deal for all member states.

Juncker, who made a point of speaking in English as he outlined the proposed settlement for the UK, said: “The commission supports this text. I have always said I wanted the UK to remain a member of the EU on the basis of a fair deal. The settlement that has been proposed is fair for the UK and fair for the other 27 member states, it is also fair for the European parliament.”

The prime minister reached out to anti-EU cabinet ministers, who believe that he is breaking the spirit of an agreement on the handling of the referendum by effectively campaigning for a yes vote. In an interview with ITV News, he said: “I’m not asking people to twist themselves in different directions and say things they don’t believe.”

Before the Commons debate, Johnson was appearing to play hard to get. “The prime minister is making the best of a bad job,” the mayor said as he left his house on his bike. “Let’s wait and see when this whole thing is agreed and try and see what it really means, every bit of it.”