David Cameron delivers his speech in Beijing Reuters

David Cameron will take a calculated gamble and tell China's leaders today that they cannot shut down debate about democracy, urging them instead to recognise that political freedom, the rule of law and a free press represent the best path to stability and prosperity.

In a speech to students in Beijing, Cameron will go further than previous British prime ministers visiting China by urging the world's new economic superpower to embrace human rights and democracy.

Downing Street said Cameron had also used a banquet last night to personally raise the issue of individual human rights abuses with the Chinese premier, Wen Jiabao – including the case of Liu Xiaobo, the jailed Chinese dissident awarded the Nobel Peace prize last month. "Of course we shouldn't be lecturing and hectoring but it is right we have a dialogue on these things," Cameron said yesterday.

No 10 said it would be counterproductive to go into details of Cameron's exchanges with Wen on the issue of Liu, but the British government was aware Liu's lawyer had been blocked by Chinese officials from flying to London yesterday on grounds of national security.

Since coming to power Cameron has been keen to put Britain's commercial interests far higher up the foreign policy agenda, and he is seeking to seal Beijing-sanctioned, multibillion-pound contracts with British companies during the visit. But as the first western leader in China since the announcement of Liu's Nobel award, he has been under growing pressure to set out the case for China to open up in its own long-term interest.

In a carefully modulated speech today, Cameron will say: "The rise in economic freedom in China has been hugely beneficial to China and to the world. I hope in time this will lead to a greater political opening because I am convinced that the best guarantor of prosperity and stability is for economic and political progress to go in step together."

In the speech, which has not been shown to, or cleared by, the Chinese authorities and is unlikely to be broadcast in Chinese media, he will refer to the virtues of British democracy. "All the time the government is subject to the rule of law. These are constraints on the government, and at times they can be frustrating when the courts take a view with which the government differ, but ultimately we believe that they make our government better and our country stronger.

"Through the media, the public get to hear from people who hold different views from the government. That can be difficult at times, too. But we believe the better informed the British public is about the issues affecting our society … the easier it is, ultimately, for the British government to come to sensible decisions and to develop robust policies that command the confidence of our people." His officials pointed out that in his previous speech in China in 2007, as leader of the opposition, he had said that he hoped by the time he returned China would have ratified and implemented the international covenant on civil and political rights, something the Chinese leadership has failed to do.

In a minor symbol of the cultural tensions between the two sides, British ministers insisted on wearing poppies at last night's reception in the Great Hall of the People in Beijing. A British official said: "The Chinese said it was inappropriate for us to wear poppies because of the opium wars. We informed them they meant a great deal to us and we would be wearing them all the same."

After five hours of talks and banqueting yesterday, Jiabao said that David Cameron's visit to China had been "fruitful". Meanwhile Cameron, who is accompanied by four cabinet ministers and 43 business leaders, called the trip a "vitally important trade mission". The jet-engine maker Rolls-Royce yesterday won a $1.2bn (£750m) contract with China – the biggest of the visit so far.

British goods currently account for only 2% of China's imports, something Cameron says he is determined to change. The chancellor, George Osborne, has said that this was not a new chapter in British relations with China, but that the country had reached a stage in its development where it was "more likely to want the things which Britain is good at".

Michael Gove, the education secretary, also signed a deal with Chinese counterparts that will extend the teaching of Mandarin in English schools. In a gauge of some Conservatives' true thinking of the degree of repression inside China, Gove, one of the cabinet ministers accompanying Cameron on his two-day visit, only a year ago condemned China as a police state with thousands killed each year by government fiat. No 10 said Gove had made his remarks when in opposition.