Miliband hoped the two nations would increase cooperation in tackling climate change and in economic and security sectors.
Britain would work with China, on the basis of mutual respect, to push forward the bilateral strategic and cooperative partnership, he said.
Miliband is visiting China from March 14 to 17 as a guest of his Chinese counterpart, Yang Jiechi.
During talks between the two foreign ministers earlier Tuesday, Yang said China-British relations were developing well, and lifting the level of the bilateral strategic dialogue would further promote bilateral relations.
"We are willing to work with Britain to further promote our comprehensive strategic partnership," Yang said.
He hoped the two nations would enhance communication and strengthen mutual understanding and mutual trust.
Yang also suggested the two nations address the financial crisis as an opportunity to actively explore cooperation in financial services, clean energy, renewable energy, energy saving and environmental protection, and to further expand investment and trade links.
Yang said the two countries should respect each other's core concerns, including those related to sovereignty and territorial integrity.
China and Britain should work together, in line with the principles of mutual respect and equality, to correctly view and properly handle differences, Yang said.
Miliband told Yang the Britain-China strategic partnership relations had maintained a sound momentum of development, and the two sides shared broad common interests and faced many common challenges.
Miliband is the first senior official from the British government to visit China this year after difficulties occured in bilateral ties at the end of last year.
The differences between the two sides should not affect the overall development of bilateral relations, Miliband said.
Miliband said Britain welcomed the inauguration of the strategic dialogue in a higher level, which was expected to "take our political cooperation to a new level."
Britain would work with China to increase economic cooperation and to jointly oppose trade protectionism, he said.
As to China-EU relations, Miliband said his country supported the European Union in promoting comprehensive strategic partnership with China.
The Iran nuclear issue was also on the agenda of Yang and Miliband. After the hour-long talks with Miliband, Yang said China hoped all parties would make concerted efforts to push for dialogue and negotiation by "adopting more constructive measures."
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