The EU’s chief negotiator, Michel Barnier, has welcomed Dominic Raab to Brussels with a thinly veiled critique of Theresa May’s Chequers plan and a 13-week deadline in which to solve the problem of the Irish border.

Appearing with Barnier for the first time in the Belgian capital, the new Brexit secretary, clutching a copy of the UK’s recently published Brexit white paper, called for more “vim, vigour and energy” in the troubled negotiations.

The former Foreign Office lawyer told reporters he was “looking forward to intensifying, heating up, the negotiations”, after stepping into the role following the resignation of David Davis over the paper, which sets out how the UK is in effect seeking to stay in the single market for goods by following a raft of EU laws.

The differing priorities between the two negotiators were clearly evident, however, as they stepped out in front of reporters together at the European commission headquarters.

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While Raab conceded there were some “gaps” in the withdrawal agreement that needed to be filled, Barnier emphasised the “urgency” of finding a solution for the most thorny issue in that deal: avoiding a hard border on the island of Ireland.

Barnier told reporters: “We have a lot of work to do with our teams. There are, as you know, 13 weeks left, before the October European council. In this time, short time, we have two things to do. We must finalise the withdrawal agreement and we are not yet there on governance.

“We must also prepare a political declaration on our future relationship. On the withdrawal agreement it is a matter of urgency to agree to a legally applicable backstop on Ireland and northern Ireland. We need an all-weather insurance policy.”

He added: “On the future relationship, the EU proposed in March an unprecedented partnership not only in economic and trade where we want an ambitious free trade agreement that respects the integrity of the market but also on internal and external security, where a close partnership between us means more important than ever given the geopolitical context.

“Our challenge will be to find common ground between the fundamental principles that define the EU and the UK positions. That is all for now, more is to come. Stay tuned.”

The two men took part in a short discussion on the UK’s white paper before dining together at the British embassy in Brussels.

Barnier gave Raab the book Going to the Mountain by Nelson Mandela’s grandson, Ndaba Mandela, as a gift.

Raab, in turn, gave the former French minister a copy of Isaiah Berlin’s The Hedgehog and the Fox. The philosopher’s most popular essay explores the difference between thinkers who view the world through a single defining idea and those who base their world view on experience.

It is understood Raab also insisted to Barnier that the Brexit talks should continue throughout the summer, despite the offer of a two-week break from the European commission.

Facebook Twitter Pinterest The meeting in Brussels on Thursday. Photograph: Olivier Matthys/AFP/Getty Images

Following his first talks with Barnier, the new cabinet minister made it clear he would be spending more time in Brussels than Davis, who spent only four hours in face-to-face negotiations with his counterpart.

Raab said: “We had a very good, constructive conversation. We talked about the progress we’ve made on the withdrawal agreement. It was also an opportunity to present the white paper on the future relationship we want with the EU.

“We’ve only got 12 weeks really left to nail down the details of the agreement, so I set out our proposals, and offered to meet with Michel Barnier throughout the summer to intensify negotiations, to get some energy, get some drive and get some heat on them to make sure we can conclude this agreement in good time. I’m sure in good faith, if that energy and that ambition is reciprocated, as I’m confident it will be, we will get there.”

Asked if a no-deal scenario was more likely after cabinet resignations, Raab declined to directly respond but said domestic battles would not undermine his role.

He said: “I think as you get closer to the line, the preparations need to be intensified.“We’re going to be increasing the preparations for no deal, but we’re focused above all on the negotiations to get the best deal.”

The meeting came as the EU issued a warning to member states in a 16-page document on the risks of a no-deal Brexit. It notes the impact of a no-deal scenario would be “very real” for citizens, and leaves open the possibility of a visa requirement for Britons travelling to the continent after Brexit should a deal not be in place..

A senior EU diplomat said the “very volatile” political situation in London and the lack of progress in the talks in Brussels on key issues had led many to believe that the risk of a no-deal scenario had increased in recent weeks.

“Contingency planning for the worst possible outcome is not a sign of mistrust in the negotiations,” the paper says. “The commission is devoting very significant resources and committing great efforts to achieve an agreement. This remains our goal. However, the outcome of negotiations cannot be predicted.”

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The UK government also appeared to be stepping up warnings about the possibility of no deal, by asking up to 250,000 small businesses who export to the EU to prepare to make a customs declaration. The idea is intended to be one of a series of public warnings issued over the summer about the possible impact of a no-deal scenario on the UK economy.

Barnier will discuss Brexit with European affairs ministers from the EU27 on Friday. An official said there would be a lot of questions on the white paper, which was “detailed but still unclear to a certain extent”.

Stressing the unpredictability of British politics, the senior EU official said they might as well “read the entrails of animals” to know what is happening.