China wants involvement in Britain's first high-speed rail line and an increased role in civil nuclear power, the country's premier said in Beijing after talks with David Cameron on the first day of the prime minister's visit.

Li Keqiang said China would also like to invest in power projects.

Speaking in the Great Hall of the People on Monday, Li said: "The two sides have agreed to push for breakthroughs and progress in the co-operation between our enterprises on nuclear power and high speed rail. The Chinese side is willing to not only participate in but also purchase equities and stocks in UK power projects."

Cameron said the scale and pace of China's transformation dwarfed Britain's industrial revolution.

The remarks by Li follow a concerted effort by Britain to mend fences with Beijing after Cameron met the Dalai Lama last year. The prime minister said last week he would welcome Chinese involvement in HS2.

Li said Britain and China were indispensable and equal partners, noting the prime minister's recent approach to Beijing by acknowledging the territorial integrity of China – diplomatic code for accepting Beijing's rule over Tibet.

Li said: "We have become indispensable partners for each other's development. China and the UK must treat each other as equals."

Cameron, who arrived in Beijing pledging to act as China's strongest advocate in the west, started the day by visiting the Chinese headquarters of Jaguar Land Rover. He then met Li at the Great Hall of the People for talks and lunch. Cameron is due to have dinner with President Xi Jinping before heading to Shanghai.

The prime minister opened his remarks at the Great Hall of the People by echoing Xi's call for a Chinese dream. The prime minister said: "China's transformation is one of the defining facts of our lifetime. The pace and scale of economic development and urbanisation dwarfs the British industrial revolution of two centuries ago. I see China's rise as an opportunity not just for the people of this country but for Britain and for the world.

"Britain wants China to realise its dream and I believe we can help each other succeed in the global race.

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 those trade barriers down."

China has rolled out a vast high-speed rail link at an astounding pace, though the reputation of the project suffered a blow with a fatal train crash near Wenzhou in 2011.

Cameron said last week that he would welcome Chinese involvement in HS2. The prime minister said during a visit to a Chinese exhibition at the V&A: "I’m very interested in what’s happening in terms of high-speed rail in China. It seems to be an absolute high-speed revolution taking place, and I’m looking forward to travelling on a high-speed train when I’m in China.

"In terms of HS2, I very much welcome Chinese investment into British infrastructure. We see already Chinese investment into Heathrow Airport, into Manchester Airport and, of course, into Hinkley Point nuclear power stations."