Boris Johnson has risked further antagonising Brussels by dismissing warnings this week about Britain’s approach to the negotiations and insisting the EU is obliged to start talking about a future trade deal.

After a bruising week for the British government, the foreign secretary expressed his “absolutely rock-solid confidence” that a deal with the 27 member states would be reached.

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In a potentially provocative move, he also explained to reporters before a meeting with his EU counterparts in Tallinn, Estonia, that the EU had a legal duty to discuss trade relations. “Article 50 makes it very clear that the discussion about the exit for a country must be taken in the context of a discussion of the future arrangements, and that’s what we are going to do,” Johnson said.

This week the EU’s chief negotiator, Michel Barnier, along with the leaders of the European parliament, publicly expressed their serious doubts that trade talks could commence in October, as planned, due to a failure to make “sufficient progress” on the divorce bill, citizens rights and the border in Ireland.

The leak to the Guardian of a Home Office document suggesting the UK wanted to limit the free movement of people from day one of Brexit further fuelled frustration in Brussels at what EU diplomats regard as Britain’s unrealistic goals.

Barnier on Thursday rejected the UK’s initial suggestions about the Irish border after Brexit, suggesting they presented a threat to the integrity of the single market.

A position paper published by the European commission setting out the EU’s aims for Ireland after Brexit said that, as the problem was of the UK’s making, it was the UK’s responsibility to come up with a “unique solution”.

However, Johnson told reporters that a suitable arrangement over the Irish border would be found between the negotiating parties and made light of the EU’s concerns. “I think we can all work together to come up with a solution to that one,” he said. “It is not beyond the wit of man. We have had a common travel area between the north and south of Ireland for getting on for a century. We are going to continue to make that work.”

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Johnson’s comments come amid growing anger at Theresa May’s decision, revealed by the Guardian, to reject an invitation to address the European parliament to explain and convince MEPs of her vision for the future.

The prime minister has insisted on talking privately to the chamber’s leaders at a date yet to be finalised rather than follow in the footsteps of Gordon Brown, Tony Blair and Margaret Thatcher and address all MEPs in a plenary session.

The Dutch Liberal MEP Sophie in ‘t Veld tweeted: “Instead of having UK officials lobby individual MEPs, @theresa_may should debate with us in public.”

The British Green MEP Jean Lambert said: “We’re meant to be transforming into a brave, new ‘global Britain’. However, our prime minister runs scared whenever she is invited to make her case in public. Theresa May’s refusal to address the European parliament is yet another signal that her political mandate is hanging by a thread.

“Perhaps it has slipped her mind that members of the European parliament will be voting on the final Brexit deal? If May doesn’t convince us that she has softened her stance on issues such as citizens’ rights, Green MEPs – and many others – will reject any agreement put to us in 2019. She would do well to involve us in discussions, rather than shutting herself away behind closed doors.”

The European parliament has the right to veto any agreement between the EU and the UK. On 2 October the chamber will vote on its latest resolution on Brexit, which will ask MEPs to agree with its leaders that there has not been sufficient progress for talks on a comprehensive trade deal to commence.