Angela Merkel has said that British travellers with two Covid-19 vaccinations will be able to travel to Germany “in the foreseeable future” without having to go into quarantine, after farewell talks with Boris Johnson.

The UK prime minister said after meeting the German chancellor he was “very confident” that British travellers given an Indian-made Oxford/AstraZeneca jab would not face problems this summer, after it emerged that the EU travel passport scheme does not recognise it.

Johnson pressed Merkel at the meeting at his Chequers country retreat on Friday to drop her hardline stance towards British travellers, who currently have to quarantine for two weeks regardless of their vaccination status.

Merkel unsuccessfully tried at a European Council meeting last month to persuade other EU countries to adopt similar measures to stop the spread of the Delta variant, which is dominant in the UK.

But speaking after a largely amicable meeting, at which Merkel addressed the British cabinet by video link, the German chancellor said the Delta variant was now also spreading quickly in her country.

“We are continually reviewing our travel restrictions,” she said, adding that in the foreseeable future people with two jabs would be able “to travel again without having to go into quarantine”.

Johnson, who paid tribute to Merkel’s contribution as Germany’s chancellor since 2005, said: “It seems as if progress is being made.” He noted that the UK also had tough restrictions on Germans travelling to Britain.

Speaking at a joint press conference, Johnson insisted that there would “not be a problem” for millions of British travellers vaccinated with an AstraZeneca jab produced by the Serum Institute of India.

The vaccine, known as Covishield, is said by experts to offer the same protection as the British-made version, but the company has not sought to secure its approval from the European Medicines Agency.

Downing Street said the UK’s medicines regulator had shared its data on the jab with its European counterpart.

EU member states can be flexible within the EU travel scheme by allowing travellers with vaccines approved by the World Health Organization, which has listed Covishield.

The meeting between Johnson and Merkel marked a new phase in British diplomacy, as Britain tries to strengthen bilateral links with individual EU member states after Brexit.

The two sides agreed to hold annual joint cabinet meetings and to bolster exchanges in areas such as culture and energy. Merkel said it was natural after Brexit that “bilateral relationships come to the fore”.

She referred to the British leader as “dear Boris” and said it was time to “open a new chapter in our relationship”. But reflecting concerns in Brussels that Johnson might try to pick off individual member states to undermine EU unity, she said: “We should not overstretch ourselves.”

Merkel, who is on her 22nd visit to Britain as German chancellor, is stepping down in the autumn and urged both the UK and EU to be “pragmatic” in finding answers to the disagreements over post-Brexit trade in Northern Ireland.

Johnson hailed a recent agreement by the EU to extend a “grace period” to allow shipments of chilled meats from Great Britain to the region, but said more work had to be done to soften the border inspection regime.

“When it comes to chilled meats the wurst is over, as Angela said,” Johnson joked. “Or maybe I said it.” The prime minister also thanked the German national football team for breaking with its tradition of beating England in major tournaments, a reference to their encounter on Tuesday in the Euro 2020 championships.

Merkel, a football supporter, replied: “This was not a voluntary offer on my side to create the right mood for this visit.” She added: “You deserved it, but we were a little bit sad.”

However, she repeated her criticism of Uefa, European football’s governing body, allowing big crowds to gather at Wembley for the semi-finals and finals of Euro 2020, saying she viewed it with “grave concern”.