British Foreign Minister David Cameron met his Chinese counterpart Wang Yi at the Munich Security Conference on Friday, the UK Foreign Office said in a statement.
Cameron told his counterpart that China should use its influence on Iran to pressure the Houthi militants over their actions in the Red Sea, the statement on Saturday said.
Cameron also set out Britain's position on human rights issues in Xinjiang and Hong Kong, raised the case of British parliamentarians sanctioned by China, and again called for the release of media tycoon Jimmy Lai.
Wang said both sides should strengthen strategic communication and play their roles in promoting security and maintaining peace, according to a statement from the Chinese foreign ministry on Saturday.
Wang also said the two sides should make joint efforts to expand "the convergence of interests" and properly handle differences and contradictions to push their relations back on the right track.
UK Prime Minister Rishi Sunak's appointment of former British leader Cameron as foreign minister last year caused concern among some lawmakers in his Conservative Party about what it would mean for the government's approach to China.
Cameron heralded a "golden era" in relations with China in 2015, something Sunak has said is over. Sunak has instead sought to balance national security interests with better cooperation on trade and climate change.
Cameron said in December last year that "the UK will continue to engage with China where it furthers our interests".
Reporting by Rishabh Jaiswal in Bengaluru; additional reporting by Albee Zhang in Beijing