While the PM is on holiday, Jeremy Hunt and Philip Hammond are due in France

A series of ministers are to head across Europe this week as the government embarks on a summer spent trying to sell Theresa May’s Brexit strategy to individual EU leaders, while simultaneously keeping sceptical Tory activists on side.

While the prime minister is on holiday in Italy, the foreign secretary, Jeremy Hunt, and the chancellor, Philip Hammond, are due separately in France in the coming days for meetings. Other ministers are also scheduled to go on trips.

Downing Street will also make renewed overtures to local Conservative associations, after it emerged that seven party chairs in areas represented by cabinet ministers have expressed scepticism at May’s painstakingly drafted Chequers plans and associated white paper.

Before May headed to northern Italy – where official photographs released on Sunday showed her strolling with her husband, Philip, by Lake Garda – she stopped off in Salzburg on Friday, as a guest of the Austrian chancellor, Sebastian Kurz.

She also held talks in Austria with the Czech prime minister, Andrej Babiš, the Estonian prime minister, Jüri Ratas, and the president of Portugal, Marcelo Rebelo de Sousa.

No 10 has talked up the discussions as a success, notably the agreement by Kurz that an informal European Council meeting in September, mainly focused on immigration, will also talk about Brexit ahead of a key summit next month.

The intention is to target politicians and voters in the individual EU27 nations in the hope of persuading them to take an easier line than the bloc’ chief negotiator, Michel Barnier, who last week who seemed to dismiss the basis of May’s customs plan, a key plank of the Chequers proposal.

“Those four meetings were all felt very positive,” a Downing Street source said. “They listened to the prime minister as she talked though the headlines of the white paper and engaged positively. And getting it to the informal European Council is going to be an important point for all European leaders to discuss that future relationship.”

May also faces challenges closer to home after a series of local party chairs, among them the head of her own Maidenhead Conservative association, told the Sunday Telegraph they either opposed the Chequers proposals outright or would not back them if the prime minister had to make concessions to the EU.

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Richard Kellaway said a briefing on the proposals at Downing Street went down well among those present. But he told the Telegraph: “I think we have reached the stage that if we don’t get a deal around these terms, then we’ll have to break away. If it were to be diluted it would ultimately not be acceptable.”

Others were more outspoken. Patricia Soby, who chairs the Tory association in Torridge and west Devon, represented by the attorney general, Geoffrey Cox, told the paper: “This constituency conducted our own survey and practically everybody was against the Chequers deal.”

Don Hammond, chair of the Conservative association in Tatton, represented by the work and pensions secretary, Esther McVey, said: “This is right at the limit of what I would consider to be a Brexit and I am distinctly unenthusiastic.”

There is acceptance within Downing Street that local party activists tend to be more heavily pro-leave, meaning some pushback is inevitable. More briefings are planned, however, in an attempt to reassure them.

The biggest setback in recent days came on Thursday when Barnier said it was not possible for the UK to collect EU tariffs as a non-member.

The EU “cannot and will not delegate the application of its customs policy and rules, VAT and duty collection to a non-member who would not be subject to the EU governance structures”, Barnier told a press conference alongside the Brexit secretary, Dominic Raab.

Downing Street has sought to play down the apparent hostility, saying Barnier had been more positive in other areas, such as the planned backstop.

“There is a chink in the Barnier armour. He’s the chief negotiator, you don’t expect him to come out with anything other than a tough line to start with,” the No 10 source said.

With the Commons in recess until 4 September, May has some respite, but lingering disquiet is likely to peak at the Conservative party’s annual conference at the end of the month. Grassroots members and refusenik MPs are likely to make their feelings plain as speculation continues that she could face a leadership challenge.