David Cameron’s hopes of blocking Jean-Claude Juncker from becoming president of the European Commission depend on a meeting next week in Sweden with Angela Merkel, Fredrik Reinfeldt and Mark Rutte.

The prime minister of the United Kingdom has staked his political reputation at home and his country’s relationship with the European Union on blocking Juncker’s appointment.

Reinfeldt, Sweden’s prime minister, has invited Cameron and his German and Dutch counterparts, Merkel and Rutte, to Harpsund, his country residence outside Stockholm, on Monday evening (9 June) to discuss the appointment of the next president of the European Commission. The meeting is scheduled to end with a news conference mid-morning on Tuesday.

Although Cameron has staked the UK’s relationship with the EU on blocking the appointment of Juncker, the former prime minister of Luxembourg saw his chances of being nominated improve significantly after Merkel  dropped her earlier reticence and came out with a statement of support for Juncker on Friday (30 May). She was forced to do so by a campaign in the German media.

Juncker is scheduled to go to the European Parliament today (5 June) to address centre-right MEPs. Officials suggest that the Commission presidency is now his for the taking and that the debate has moved to finding a president of the European Council who is acceptable to Cameron, such as Helle Thorning-Schmidt, Denmark’s prime minister. “Having someone like Thorning-Schmidt in the Council could make up for some of the damage of having Juncker in the Commission,” said Charles Grant of the Centre for European Reform, a think-tank in London.

It would be a humiliating defeat for Cameron if the European Council on 27 June outvoted the UK and appointed Juncker. Such a move would embolden Eurosceptic backbenchers in Cameron’s Conservative Party and make it more difficult for the prime minister to resist calls for an early referendum on leaving the EU. Cameron is supposed to have warned Merkel at last week’s summit that a Juncker appointment would accelerate moves toward a British exit.

“The man is desperate, his whole strategy of keeping the UK in the EU is in trouble,” Grant said about Cameron. “I’m not going to defend his tactics, but what he says is true – keeping the UK in the EU will be much more difficult with Juncker as [Commission] president.”

Cameron is now seeking to bolster the anti-Juncker front inside the EU and the meeting at Harpsund is critical to that endeavour, but it looks increasingly unlikely that he will be able to block Juncker. Grant said about the Harpsund meeting: “This is the moment when Reinfeldt and Rutte really have to make Cameron’s case to Merkel – because they can make it better than Cameron – and ask, is he serious about economic reform in the Union and shaking up the Commission?”

At last week’s informal summit of national leaders in Brussels, three prime ministers in addition to Cameron spoke out against Juncker:  Rutte, Reinfeldt, and Viktor Orbán of Hungary. Reinfeldt and Orbán are both members of the centre-right European People’s Party that nominated Juncker, as is Merkel.

Hungary, the Netherlands, Sweden and the UK together would fall short of a blocking minority in the European Council should it come to a vote on Juncker’s appointment on 27 June. However, it would be politically awkward for the Union to appoint a Commission president against the wishes of three or four member states. “Qualified-majority voting is only a way to lead to a reasonable discussion, and [to ensure] that there cannot be blackmail,” an EPP adviser said. A national diplomat said: “Outvoting one member state is one thing, but outvoting several is a different thing altogether.”

In an address to parliament yesterday (4 June), Merkel backed Juncker’s nomination but also stressed the importance of the UK staying in the EU. “Just like the whole federal government, I work toward Jean-Claude Juncker becoming Commission president,” she said. But she also said: “It is far from irrelevant whether the UK stays in the European Union.”

Merkel reiterated that according to the EU’s Lisbon treaty, it is up to the national leaders in the European Council to nominate a Commission president. “We never had any doubts about her backing,” a source close to Juncker said. He said her backing was “not out of love, it was a rational choice”.

Merkel’s refusal explicitly to back Juncker’s appointment as Commission president  – led to hostile questioning from German journalists at the end of last week’s Brussels meeting.

Herman Van Rompuy, the president of the European Council, is now holding meetings with various European leaders, first on the sidelines of a G7 summit that started in Brussels yesterday (4 June), then in the margins of D-Day commemorations in Normandy tomorrow (6 June), and finally in Kiev on Saturday, during the inauguration of Petro Poroshenko as Ukraine’s president.

Van Rompuy “is testing with the Parliament if the choice that has the backing of a qualified majority [of member states] also gets an absolute majority in Parliament”, an official said.

Manfred Weber, who was elected leader of the EPP group in Parliament with a sweeping majority yesterday, said that he would start negotiations with the centre-left Socialists and Democrats on a work programme for a Juncker-led European Commission. Juncker is expected to address EPP MEPs in Brussels today.