Theresa May’s first official visit to China has been long in the making, but when the prime minister finally met Xi Jinping, the leader of the world’s second largest economy, the most talked-about moment was how she and her husband had remarked that they enjoyed the same tea at home as was served by the president.

Earlier in the day, with May’s leadership under intense scrutiny at home, the international trade secretary, Liam Fox, went out to bat for the prime minister in Beijing, telling broadcasters that “her middle name is resilience” and critics on the backbenches should pay attention to her on the world stage.

However, there has been little to hold their attention on this visit. Most significant announcements have been vague. May said she had secured agreement to open up the Chinese market for new financial services. Fox said the business delegation had signed £9bn in new deals with the Chinese, though not all details have been made public. He also heralded the commitment to start a joint trade and investment review, exploring new trading partnerships which could eventually pave the way for free-trade talks.

By comparison, on Xi’s state visit to Britain in 2015, the total value of deals signed was £40bn, according to a House of Lords library report. And Fox himself conceded that any future trade deal was “some way off”.

At her press conference with the premier, Li Keqiang, there was also a promise of new routes for British agricultural produce for the Chinese market, and a pledge to explore lifting the ban on British beef, which has been in place since the BSE crisis in the 1980s.

However, announcements from Li were carefully worded to subtly stress his country’s upper hand. China, he said, was already self-sufficient in agriculture but Chinese consumers should have a choice to buy British.

“China is a major agricultural country and we have supply from our own market but we would like to give them more options, so we would like to buy more agricultural products from the UK,” he said.

The balance of the relationship is not new. China has long been eager to make clear its self-sufficiency, especially to the British, dating back to a famous letter from Emperor Qianlong to King George III in 1793.

“As your ambassador can see for himself, we possess all things. I set no value on objects strange or ingenious, and have no use for your country’s manufactures,” he wrote.

Apart from the promise of a trade review, the majority of announcements from Downing Street during the three-day trip were focused on soft power, namely educational, culture and environmental partnerships.

Among them were the extension of an existing scheme to send British maths teachers to learn from their Chinese counterparts, a campaign to promote English language learning, a pledge to tackle ivory smuggling, the sale of distribution rights to the BBC series Poldark and a new Eden Project initiative in a former limestone mine in Jizhou, near the city of Tianjin. Downing Street said the cultural deals would generate 2500 jobs.

Vince Cable, the Liberal Democrat leader who visited China in 2010 as the then business secretary when David Cameron and George Osborne were courting the country, said Brexit had damaged Britain’s ability to negotiate as an equal power.

“Theresa May is learning that trade deals won’t fall like ripened fruit into her hands. China is very much aware that the Brexit vote has weakened the UK relative to the EU and that is reflected in the comparatively modest announcements we are seeing today,” he said.

“This is not unique – India made it brutally clear that any trade deal with the UK will be dependent upon reforms to the visa system for Indian citizens.”

Fraser Howie, the co-author of books about China’s economic rise, said he suspected the economic gains of May’s trip would be “grossly overhyped” and turn out to have limited impact. Beijing was a master of committing to deals that failed to materialise once the media’s focus moved elsewhere.

“Theresa May obviously is looking for China to give her some sort of Brexit get-out-of-jail-free card,” Howie said. “[But] I don’t think Beijing has to offer anything, frankly, because they have all the cards. They are in a strong position. Britain has absolutely zero leverage over China. The whole Brexit thing does not even allow Britain to be a back door into the EU.”

Mark Malloch Brown, the former United Nations deputy secretary general who chairs the pro-remain Best for Britain campaign, said the agreements were thin. “Britain under Theresa May seems to think that it’s either EU or China. Now Mrs May is desperately mopping up any trade opportunity we can find to cover the self-inflicted wound of Brexit. Every trade deal struck is welcome but will not triage the Brexit wound.”

May, not a natural diplomat who enjoys pressing the flesh on flashy overseas tours, has taken a firmer stance with her Chinese hosts than Cameron and Osborne, though she still uses their favourite phrase, “golden era” of British-China relations.

Her more cautious approach to China was kicked off early in her premiership by a shock decision to pause the £18bn Hinkley Point scheme, which is jointly funded by a Chinese nuclear firm.

Her then joint chief of staff Nick Timothy was among those said to be sceptical about Chinese involvement in key infrastructure development. The project eventually got the green light but not before China’s ambassador suggested “mutual trust” was under threat.

In Beijing, May sidestepped a Chinese push for a formal endorsement of its $900bn Belt and Road Initiative, suggesting Britain still has concerns about China’s political objectives for the huge infrastructure project. The decision not to sign the memorandum of understanding was fudged in the Chinese press. China Daily wrote that the UK had “witnessed the signing of a memorandum” on the Belt and Road Initiative, which initially caused confusion, but turned out to be a funding deal with Standard Chartered Bank.

May told reporters she had raised the deterioration of human rights in Hong Kong with Xi during their 80-minute meeting, and Downing Street said she had brought up specific cases of concern. If May intended to strike a harder line, however, the effect was not felt across Chinese state media.

The Global Times, a mouthpiece of the government, said China believed May had bowed to pragmatism rather than calls to stand up to Beijing. “Some western media outlets keep pestering May to criticise Beijing in an attempt to showcase that the UK has withstood pressure from China and the west has consolidated its commanding position over the country in politics,” it said. “May will definitely not make any comment contrary to the goals of her China trip … For the prime minister, the losses outweigh the gains if she appeases the British media at the cost of the visit’s friendly atmosphere.”