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Theresa May has agreed a joint trade and investment review with China as the first step towards an "ambitious" post-Brexit deal, Downing Street said.

The prime minister said "we will be free to strike our own trade deals" after leaving the EU, following talks with China's President Xi Jinping.

Mr Xi said China's markets would be further opened to the UK, including in beef, dairy and other food products.

Mrs May said £9bn in business deals would be signed on her three-day trip.

There was no specific discussion of a particular model for a trade deal between the two countries after Brexit during the two leaders' 80 minute meeting, Downing Street said.

But the point of the review agreed by the two countries was to look at what model could work best, a spokesman said.

Mrs May and Mr Xi also discussed their shared determination to end illegal nuclear activity by North Korea and agreed that denuclearisation was the objective, Downing Street said.

In the wake of democracy protests in Hong Kong, they restated their commitment to the "One Country, Two Systems" arrangement in place since the former colony was handed back by the UK to China in 1997.

Stressing that he was looking forward to building on the success of the UK-China relationship, Mr Xi quoted Shakespeare, saying: "What's past is prologue."

Mrs May "pointed to the joint trade and investment review which will now take place as the first step towards delivering ambitious future trade arrangements", Downing Street said.

The two leaders also agreed to hold more talks on China's Belt and Road infrastructure initiative at their meeting, which was also attended by the UK's International Trade Secretary Liam Fox.

Mrs May and Mr Xi agreed the importance of having frank conversations in areas where the two countries do not see eye-to-eye, Downing Street said in a statement.

Talks between the two leaders were followed by a traditional Chinese tea ceremony for Mrs May and husband Philip, hosted by President Xi and China's First Lady Madame Peng and a dinner at the Diaoyutai State Guesthouse.

The UK prime minister is in China at the head of a 50-strong business delegation.

Image copyright Getty Images Image caption Theresa May outside the British Embassy in Beijing

Mrs May is understood to have raised environmental issues with Mr Xi - and she presented him with a box-set of the BBC's Blue Planet II series, with a personal message from presenter Sir David Attenborough.

The show examined the effect of human behaviour on the environment and was referenced by Mrs May last month when she pledged to eradicate all avoidable plastic waste in the UK by 2042 as part of a 25-year green strategy.

On the first day of her trip the prime minister announced a UK-China effort to strengthen international action against the illegal trade in ivory.

UK-China trade is currently worth a £59bn a year.

One of the UK companies travelling with the PM, health-tech firm Medopad, has said it signed more than £100m of commercial projects and partnerships with organisations including China Resources, GSK China, Peking University and Lenovo.

Fox urges Tories to focus on the 'big picture'

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By Laura Kuenssberg, political editor

International Trade Secretary Liam Fox is in China and wants his restive colleagues at home to focus on the big picture.

Listing the number of deals that have been done already this week during the prime minister's visit he told me that building levels of trade with China is a real "success story".

No 10 is confident that by the end of this marathon trip well over £9bn of new contracts will have been secured - such a high profile political investment edging deals over the line.

Read more from Laura