Britain will act as China's strongest advocate in the west, David Cameron has declared as he flew into Beijing pledging to lead a "dialogue of mutual respect and understanding".

In a sign of Downing Street's determination to appease Beijing, which was furious when Cameron met the Dalai Lama last year, the prime minister said no country was more open to China as he called for a new EU-China free trade agreement.

Writing in the Chinese weekly news magazine Caixin, Cameron said: "Put simply, there is no country in the western world more open to Chinese investment, more able to meet the demands of Chinese consumers, or more willing to make the case for economic openness in the G8, the G20 and the European Union. And there is no country more ready to forge a dialogue of mutual respect and understanding that can address issues of concern and advance our shared interests in the world."

The PM's effusive praise for China came as he landed in Beijing at the head of Britain's largest overseas trade and ministerial mission, designed to restore full relations after his meeting with the Dalai Lama.

The delegation includes the architect Zaha Hadid, ex-England footballer Graeme Le Saux, Arts Council England chair Sir Peter Bazalgette, the chief executive of Jaguar Land Rover, Ralf Speth, and Karren Brady, vice-chairman of West Ham United.

But Cameron came under fire from Labour for including figures close to him in the delegation. On the trip are his stepfather-in-law, Viscount Astor, representing Silvergate Media; the Tory peer Lord Chadlington, who helped to house the Camerons when the PM first fought the parliamentary seat of Witney; and the Tory donor and peer Lord Leigh of Hurley, of Cavendish Corporate Finance.

Jon Ashworth, the shadow Cabinet Office minister, said: "Whether it's dinners for donors or jetsetting trips for his friends, David Cameron rarely misses a trick to favour those close to him. Meanwhile, everyone else is offered no respite from the everyday reality of the Tory cost of living crisis."

Cameron will meet the new Chinese president Xi Jinping and the new premier Li Keqiang for separate talks in Beijing on Monday. He will hold talks, followed by lunch, with the premier at the Great Hall of the People. In the early evening Cameron will hold talks with the president followed by dinner at the State Guest House.

The prime minister will then travel to Shanghai on Monday night and will visit Chengdu on Wednesday before returning home ahead of George Osborne's autumn statement on Thursday.

The PM said he was best placed to champion China in the west, months after China and the EU came close to a trade war after Chinese firms were accused of dumping €21bn (£17.4bn) of solar panels at below cost price last year. An EU threat of punitive duties prompted China to threaten sanctions on German cars and French wine.

EU and Chinese leaders launched negotiations on a bilateral investment treaty at the 16th EU-China summit in Beijing last month to increase bilateral trade from about $580bn (£350bn) in 2012 to $1tn by 2020. But there is deep scepticism in Brussels at the idea of an EU-China free trade deal amid fears that China would use it to flood the market with cheap goods. The EU is China's biggest export market, while China is the EU's second-biggest export market.

In his article for Caixin, Cameron swept aside recent EU concerns over Chinese rules that mean Europeans must work with a Chinese joint venture partner and hand over sensitive technology. The European commission highlighted concerns over China in May when it said it was prepared to launch an anti-dumping and anti-subsidy investigation into Huawei, the world's second-largest telecoms equipment manufacturer.

The prime minister, who said an EU-China free trade agreement would be worth £1.8bn a year to the UK alone, wrote: "China's transformation is one of the defining facts of our lifetime. Last year China became the world's largest trading nation. Next year China is set to become the world's largest importer of goods and later this century it will become the world's biggest economy.

"We should be clear that there is a genuine choice for every country over how to respond to this growing openness and success. They can choose to see China's rise as a threat or an opportunity. They can protect their markets from China or open their markets to China. They can try and shut China out – or welcome China as a partner at the top table of global affairs."

On the proposed free trade agreement, he wrote: "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."

The Labour leader, Ed Miliband, is to warn that there is no point in trying to compete with China on low wages. Talking to staff at the VW National Training Centre in Milton Keynes he will say: "David Cameron needs to understand a simple truth: we're not going to win a race with China by winning a race to the bottom, by competing on low pay and low skills. And, if we try, it will be the people of Britain who lose."

He will say the UK should "compete on the basis of high-skill, hi-tech, high-wage economy – encouraging small businesses who want to grow, helping young people like you who want to get on and businesses like these which want to train, backing the real wealth creators in our country".

Maria Miller, the culture secretary, who is accompanying the prime minister, will announce an agreement between the Premier League and the Chinese Super League to build up elite football at community level.