"The UK and China will not always see eye-to-eye", May said.
"British businesses are keen to play their part in further deepening and engraining the economic ties between China and the United Kingdom".
Downing Street said that the scheme which is seeing China invest billions of pounds in infrastructure in Asia and Europe, could contribute to global growth if it was "well implemented", but said that it had to meet "international standards".
May began her visit in the central industrial city of Wuhan and will be in China until Friday in what the Chinese foreign ministry has touted as a "historic visit".
She will hold talks with President Xi Jinping on Thursday and finish her visit Friday in the eastern business hub of Shanghai. The topic, "human rights in Hong Kong" yet remains debatable whether should be discussed or not.
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Amnesty International UK's head of policy and government affairs, Allan Hogarth, said it was vital the PM did not "shirk from raising China's appalling human rights record".
Her remarks, warning China to respect worldwide rules if it wants to trade with the West, while couched in the meekest possible terms, will risk irritating Beijing.
The U.K. and China both supported a strong and united Europe as being in the interests of both countries; yet leaving the European Union means "Britain will be free to make its own decisions over its trade and investment partnerships", she said.
A series of business deals are expected to be signed during the trip, which May and her International Trade Secretary Liam Fox will hold up as examples of the positive future which lies ahead for the United Kingdom after Brexit.
The prime minister, who will be accompanied by her husband Philip for the first time on a visit outside Europe, said she would push for greater commitments from the Chinese to adhere to global economic rules and standards as it continued to "open up" to the world.
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"One of the things the prime minister will be focusing on this visit is looking at the scope to work with China, as China opens up its markets, to move towards a more ambitious trading relationship with China", Woodward told reporters. "And I want to see that this happens in a way that protects our values, ensures global security, and advances the multilateral system and the rules for which we have fought so hard".
"That job is about getting the best Brexit deal, about ensuring that we take back control of our money, our laws, and our borders, that we can sign trade deals around the rest of the world".
There were more cautionary words on China's human rights record and concerns over democracy in the former British colony of Hong Kong, which the United Kingdom returned in 1997 on a promise to maintain the city's "high degree of autonomy" for 50 years. So at least in this respect, Mrs May has to impress not only her hosts, but also her domestic audience. The committee that holds the letters does not comment on the actual number.
She leaves behind a divided government, a feuding Conservative Party - and a question mark over how long she will remain leader once she returns.
Since then the pressure has been amplified by gaffes, scandals, and a growing concern among some that constant infighting over Brexit was drowning out attempts to win back the voters the party lost at the 2017 election. "Yes, we need to ensure that we do speak about the achievements that we've seen". What we're doing now is doing the job that the British people asked the Government to do which is to deliver on Brexit.
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Worst experience, American Air. - Jen Selter (@JenSelter) January 28, 2018I did nothing wrong but got kicked off the plane. A flight attendant reportedly asked Selter asked if she wanted to be removed from the flight, to which she said yes.