David Cameron has promised to create a "partnership for growth and reform" as he visits China on a trade mission with more than 100 UK business leaders.
The PM, who met Chinese Premier Li Keqiang on Monday, also pledged to put his "full political weight" behind a proposed EU-China trade agreement.
On Tuesday, Mr Cameron urged business people at a lunch in Shanghai's business centre to invest in the UK.
He said the UK and China had "deep complementary economies".
"If you are investing in Britain, invest more," he said.
"If you are thinking of investing in Britain, come and find us. You will get a warm welcome."
He won applause as he outlined plans for same-day visas for business visits to the UK and later tried his hand at speaking Mandarin,
On Monday, Premier Li Keqiang said the pair had agreed in their talks to "push for breakthroughs" on nuclear power and high-speed rail.
The leaders read out statements to reporters after their talks in Beijing's Great Hall of the People, but did not take questions.
Mr Li said the talks had been "highly productive", adding that the UK and China had become "indispensible partners for each other's development".
"On infrastructure, the two sides have agreed to push for breakthroughs and progress in co-operation on our enterprises in nuclear power and high-speed railway," he continued.
"The Chinese side is willing to not only participate but also purchase equities and stocks in UK nuclear power projects, and the UK side is open to this idea."
Mr Li and Mr Cameron announced that they had also agreed a £200m research fund aiming to foster scientific collaborations.
The UK PM said: "I see China's rise as an opportunity not just for the people of this country but for Britain and the world.
"Britain wants China to realise its dream and I believe we can help each other succeed in the global race."
Mr Cameron criticised opponents of trade liberalisation with China.
"Some in Europe and elsewhere see the world changing and want to shut China off behind a bamboo curtain of trade barriers. Britain wants to tear these trade barriers down," he said.
"An open Britain is the ideal partner for an opening China... No country in the world is more open to Chinese investment than the UK."
Mr Cameron promised to "champion an EU-China trade deal with as much determination as I am championing the EU-US trade deal".
He believes the EU deal could be worth "tens of billions" of pounds a year - including £1.8bn for the UK alone.
Writing in Chinese magazine Caixin, Mr Cameron declared his ambition to use this week's visit to help forge "a partnership for growth and reform that can help to deliver the Chinese dream and long-term prosperity for Britain too".
He welcomed signals from last month's third plenum of the ruling Communist Party that China wanted to open up more under the leadership of President Xi Jinping, who took up office a year ago.
Mr Cameron added: "Britain is uniquely placed to make the case for deepening the European Union's trade and investment relationship with China.
"Building on the recent launch of EU-China negotiations on investment, and on China's continued commitment to economic reform, I now want to set a new long-term goal of an ambitious and comprehensive EU-China free trade agreement.
"And as I have on the EU-US deal, so I will put my full political weight behind such a deal which could be worth tens of billions of dollars every year."
Mr Cameron believes that eliminating tariffs in the 20 sectors where they are highest, such as vehicles, pharmaceuticals and electrical goods, could save UK exporters £600m a year.
During the first day of his second trip to China as prime minister, he also attended the official opening of a new academy in Beijing for training technicians, salesmen and service staff for Jaguar Land Rover, which is signing a £4.5bn agreement to provide 100,000 cars to the National Sales Company over the next year.
JLR chief executive Ralf Speth is among the 120-strong business delegation accompanying Mr Cameron, along with executives from major exporters like Rolls-Royce, BP, Royal Dutch Shell, Barclays, HSBC, GlaxoSmithKline, Arup and Virgin.
But figures from smaller businesses, such as Westaway Sausages of Devon, Moulton bicycles and the Cambridge Satchel Company make up the bulk of the party.
Mr Cameron said: "I hope that by advancing and extending our bilateral trade, by working together on the global issues that affect us all and by maintaining an honest and open dialogue, my visit to China can plant the seeds of a long-term relationship which will benefit China, Britain and the world for generations to come."
The visit represents a warming of relations after a dispute over the prime minister's decision to meet the Dalai Lama in May.
And it comes six weeks after Chancellor George Osborne led a business delegation to China.
The UK opposition leader Ed Miliband warned that the government thought "that for the majority, insecurity, low pay and squeezed wages are simply an immutable fact of life, the only way we can compete".
He said: "The only way we can compete with China - and the only way Britain can win - is by winning a race to the top.... where we compete on the basis of high-skill, high-tech, high-wage economy."
The UK Independence Party's leader Nigel Farage said that the UK was being constrained by its membership of the European Union.
"We should be carving out trade deals to suit our businesses, our expertise, our interests and needs, not having to comply with a compromise designed to accommodate the whole EU including those inside the failing Eurozone," he said.
Mr Osborne's Autumn Statement, which sets out the UK government's tax and spending proposals, has been put back 24 hours to accommodate Mr Cameron's trip, and will take place this Thursday, instead of Wednesday.