Theresa May has told Xi Jinping their countries have a collective responsibility to do more on plastic waste as she met China’s president in Beijing.



The prime minister, who spent part of her visit viewing a British initiative to remove tiny particles of plastic from the Yangtze river, stressed the importance of the Paris climate change agreement in her meeting with the Chinese leader, whom she had earlier given a box set of the BBC’s hit series Blue Planet II.



In the meeting on Thursday the two leaders discussed the situation in Hong Kong, raised by May, amid growing concerns about the deterioration of free speech and democracy. No 10 said Xi and May agreed to reaffirm their commitment to “one country, two systems”, but Xi appeared to give no concrete assurances.



“The PM and president agreed the importance of having frank conversations in areas where the two countries do not see eye to eye,” Downing Street said after the meeting as May flew on to Shanghai, where she will spend the last day of her tour. “They looked forward to further deepening their ties in the ‘golden era’, including in areas such as culture and education.”



May also stressed the growing trade links between China and the UK but struck an overall positive note in a brief outline of the meeting, praising China as an “outward-looking country”.



May and her husband, Philip, later took part in a traditional tea ceremony with Xi and his wife, Peng Liyuan, after the 80-minute bilateral meeting.



When the British visitors were served Lapsang Souchong tea, Philip May exclaimed it was the same tea that the couple drank in Downing Street, telling Peng: “We drink that.”



The pair met for talks at the Diaoyutai state guesthouse in Beijing on the second day of May’s first bilateral trip to China, which covered foreign affairs and security, as well as trade and cultural links.



“As we both sit together as permanent members of the security council of the United Nations, there are global challenges which we both face, as do others in the world,” she said.



Facebook Twitter Pinterest Theresa May and the British delegation meet with Xi Jinping at the Diaoyutai state guesthouse in Beijing . Photograph: Wu Hong/AFP/Getty Images

“As you say, there are areas in which we can work together. I’m very pleased to be able to be here in China, to take further forward the global strategic partnership that we have established.”



The prime minister opened the talks praising the “golden era of UK-China relations” – a phrase first used by David Cameron and George Osborne during Xi’s state visit to the UK in 2015.



“Since then I think we have indeed achieved a great deal in enhancing the links between our two countries, both in terms of people links and also trading links – we now see trade valued at nearly £60bn [with] 600,000 visas issued to Chinese visitors to the United Kingdom,” May said, seated across the table from Xi and backed by the British and Chinese delegations.



“I welcome the investment that has been made in the United Kingdom but also the growing trade links that we have between our two countries.”



May said the visit had been “very successful” for the large business delegation that accompanied her. “But as you say the links between us go beyond trade. I’m very pleased with the people-to-people links we have been able to build on in education and in culture, too. Also as you say, we are both significant players on the world stage of outward looking countries.”



Earlier in the day, May visited the Forbidden City and hosted a business reception at the British embassy. In an interview with Chinese television, where she delivered a New Year message, the reporter revealed Chinese commentators online had given her a nickname “Auntie May”.



Facebook Twitter Pinterest Theresa May and her husband, Philip, visit the Forbidden City. Photograph: Dan Kitwood/Getty Images,

“A lot of Chinese people would affectionately call you, in Chinese, ‘Auntie May’, the interviewer said. “That’s really a kind of a call for Chinese – you’re one of the members of the family. Do you like that?”



“I’m honoured by that,” May said. “Thank you.”



Earlier on Thursday, the international trade secretary, Liam Fox, said the Chinese had a positive image of the prime minister, contrasting it with her struggles with the Conservative party at home. Fox said that was not the image Chinese leaders had of May.



“They are looking at performance, they are looking to see what the UK is doing and they look at the prime minister in a different way than some of, let’s say, the internal tea room discussions in the UK do,” he told the BBC.



“I sometimes wish that first of all people could see the prime minister the way that she’s seen in other countries in terms of the vision that she’s put forward for Britain and, secondly, I wish they could see Britain in the way that the rest of the world sees us and not the some of the internal commentators in the UK.”