Prime minister makes last-ditch effort to persuade London mayor to join his campaign as he sets out case to stay in Europe

David Cameron is mounting a last-ditch effort to woo London mayor Boris Johnson to back his campaign to stay in the European Union, by drawing up plans for a new constitutional settlement that puts the sovereignty of British institutions beyond doubt.

Speaking outside 10 Downing Street, the prime minister confirmed on Saturday that the in/out referendum on the UK’s membership will be held on Thursday 23 June, after he returned from Brussels with a final deal that he said gave Britain a “special status” within the EU.

Admitting that he felt no “love” for Brussels, Cameron said the changes he had achieved would not solve all the frustrations he and many others felt towards the EU, but were a big step in the right direction. They would ensure that the UK would never be part of an EU superstate or join the euro.

Addressing the British people directly, as he announced the first British referendum on the EU since 1975, he said: “The choice is in your hands. But my recommendation is clear. I believe that Britain will be safer, stronger and better off by remaining in a reformed European Union.”

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Since the tortuous final leg of negotiations on Thursday and Friday came to a close, Cameron has been rocked by a decision by justice secretary, Michael Gove, to join the Leave campaign.

Gove, one of the heavyweight figures in the cabinet, confirmed his decision in a statement saying: “The European Union prevents us being able to change huge swaths of law and stops us being able to choose who makes critical decisions which affect all our lives. Laws which govern citizens in this country are decided by politicians from other nations who we never elected and can’t throw out.”

Downing Street is now nervously awaiting the verdict of the mayor of London, who, the Observer understands, intends to make a statement on Sunday night on which side he will back. If both Gove and Johnson, two of the best communicators in Tory ranks, side with the out campaign, many MPs believe the prime minister will face an uphill struggle to convince voters that their best interests lay in remaining inside the EU.

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Sources close to Johnson said he remained “genuinely torn” and that he would “chew over” what the prime minister has to say when Cameron appears on the BBC’s Andrew Marr Show on Sunday, before issuing some form of statement this evening. He will then spell out the reasons for his decision in his column for the Daily Telegraph on Monday.

It was also reported that Gove and Johnson met on Tuesday evening, as the prime minister was finalising the UK’s renegotiated membership of the EU, to discuss their position on the referendum. According to the Mail on Sunday, the pair decided the deal agreed in Brussels was “thin”.

Cameron is now working up plans that would give legal guarantees of the sovereignty of UK institutions over EU ones. Speaking in his late-night press conference before leaving Brussels on Friday night, Cameron said the government “needed to go further to put Britain’s sovereignty beyond any doubt”.

He added: “I will shortly be bringing forward further proposals that we can take as a country, unilaterally, to strengthen the sovereignty of Britain’s great institutions.”

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Progress on drawing up the plans has been discussed between Cameron and Johnson although it is not know whether they will be sufficiently robust to prevent the mayor backing Brexit.

On Saturday Cameron won the backing of home secretary Theresa May, who some had feared would back the out campaign. She said: “The EU is far from perfect, and no one should be in any doubt that this deal must be part of an ongoing process of change and reform – crucial if it is to succeed in a changing world.

“But in my view – for reasons of security, protection against crime and terrorism, trade with Europe, and access to markets around the world – it is in the national interest to remain a member of the European Union.”

Facebook Twitter Pinterest Michael Gove poses for a photograph with activists attending the launch of the Vote Leave campaign at the group’s headquarters in central London on Saturday. Photograph: Stefan Rousseau/PA

The prime minister will make a statement to the House of Commons on Monday about his renegotiation and plans for the June referendum. On Saturday after a cabinet discussion that was described as “dignified” – despite several ministers making it clear they would campaign for out – Cameron said it would be folly for the UK to leave the EU at a time of deep uncertainty over global security and the economy.

“The question is will we be safer, stronger and better-off working together in a reformed Europe or out on our own?” he said. “I believe we will be safer in a reformed Europe, because we can work with our European partners to fight cross-border crime and terrorism.

“I believe Britain will be stronger in a reformed Europe because we can play a leading role in one of the world’s largest organisations from within, helping to make the big decisions on trade and security that determine our future.

“And I believe we will be better off in a reformed Europe because British businesses will have full access to the free-trade single market, bringing jobs, investment and lower prices. Let me be clear: leaving Europe would threaten our economic and our national security.”

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In an apparent sideswipe at Gove and others who have refused to back him, he added: “Those who want to leave Europe cannot tell you if British businesses would be able to access Europe’s free-trade single market or if working people’s jobs are safe or how much prices would rise. All they are offering is risk at a time of uncertainty – a leap in the dark.”

Writing in the Observer, Labour leader Jeremy Corbyn makes a strong case for remaining in the EU: “Being part of Europe has brought Britain investment, jobs and protection for workers, consumers and the environment.

“We are convinced that the EU is a vital framework for European trade and international cooperation in the 21st century, and that a vote to remain in Europe is in the best interests of our people.”

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But, he says, the prime minister’s strategy has been “to protect his friends in the City of London from financial regulation, including of bankers’ bonuses. Cameron’s Tories want a free-market corporate Europe. We want a social Europe of decent jobs and equality for all.”

Commons leader Chris Grayling, another out campaign backer, said: “I actually believe the EU is holding this country back. We cannot control our borders, limit the number of people who come here, do trade deals. I do not believe we can take decisions in the national interest when we are part of the European Union.”

Culture secretary John Whittingdale, work and pensions secretary Iain Duncan Smith, Northern Ireland secretary Theresa Villiers and employment minister Priti Patel have also joined the Leave campaign.