China’s domestic stock market may be in turmoil but the country’s currency, known as the yuan or renminbi, is making a seemingly relentless push deeper into the global financial system.

The latest step: the London Metal Exchange, the world’s largest venue for trading metals where $15 trillion of metals was traded last year, is set to accept yuan as collateral for banks and brokers that trade on its platform. The Chinese currency joins the U.S. dollar, the euro, the British pound and Japan’s yen, which are all currently permissible...