The Chinese premier, Wen Jiabao, issued a diplomatic dressing down of the British government by declaring the UK should stop "finger pointing" over human rights in discussions with Beijing.

Wen also suggested the UK economy needed to do better, in remarks that appeared to differ from his warm words towards Germany, which he was also visiting on his European tour.

The rebukes marred the signing of some £1.4bn of trade deals, the most important being an agreement between BG, the UK energy group, and Bank of China for up to $1.5bn of funding to expand projects in China.

Britain, for its part, said it would welcome Chinese investment in UK infrastructure, as well as greater co-operation over international development.

At a Downing Street press conference, Wen repeatedly aired his frustration at the way the UK government and media seemed to obsess about human rights.

He said: "On human rights, China and the UK should respect each other, respect the facts, treat each other as equals, engage in more co-operation than finger-pointing and resolve our differences through dialogue. China is not only pursuing economic development but also political structural reform and improvement in democracy and the rule of law."

He said China had been exposed to untold sufferings in its 5,000-year history. "This has taught the Chinese never to talk to others in a lecturing way, but to respect nations on the basis of equality."

David Cameron said: "We applaud the economic transformation that has taken place in China … But, as I said in Beijing last November, we do believe the best guarantor of prosperity and stability is for economic and political progress to go in step together."

The prime minister said no issue had been left off the table but No 10 was reluctant to detail specific human rights abuses. He said: "There is no trade-off in our relationship. It is not about either discussing trade or human rights. Britain and China have such a strong and developed relationship. We have a dialogue that covers all these issues, and nothing is off limits in the discussions that we have."

Wen did say there was "no strategic conflict" between the UK and China and that "our common interests outweigh our differences". It was a mark of this relationship that China would be sending two giant pandas, Tian Tian and Yangguang, to Edinburgh Zoo by the end of this year – as announced by China's vice premier, Li Keqiang, in January.

Cameron also pressed China to crackdown on abuses of intellectual property and patents, saying it was "absolutely essential" because of Britain's strength in branded goods and in film, music and the arts. A "symposium" to discuss the issue has been set up.

Chinese officials, involved in a month-long crackdown on civil rights activists, expressed irritation and said Britain was viewed less favourably in Beijing than Germany, France, Italy and Spain. There is anger that Cameron may have gone further than other European leaders when in China in raising human rights concerns.

In a speech to the Royal Society, Wen admitted corruption and income disparities were harming people's lives in China. "Without freedom there is no real democracy and without the guarantee of economic and political rights there is no real freedom," he said. "To be frank, corruption, unfair income distribution and other ills that harm the people's interests still exist in China."

Wen also expressed his differences with the British over Libya saying the solution lay in diplomacy. "Foreign troops may be able to win war in a place, but they can hardly win peace. Hard lessons have been learned from what has happened in the Middle East and Afghanistan."

China still supported the UN security council resolution that authorised air strikes to protect civilians, but the nations involved must comply with the strict terms. Wen added: "We hope that the issue of Libya will be resolved through political, peaceful means, to reduce the humanitarian harm and in particular the harm of innocent civilians."