Legal action against British American Tobacco (BAT), one of the world’s largest tobacco firms, could see the company punished for profiting from child labor and force the industry to finally confront its treatment of vulnerable workers.

The case, brought by human rights lawyers on behalf of hundreds of tenant farmers and their children in Malawi, contends that the company is guilty of “unjust enrichment.”...The claimants are suing for compensation, and their lawyers believe it could force the company to pay more for the leaf it buys to ensure proper livelihoods for the workers and farmers at the bottom of its supply chain.

BAT said it takes the issue “extremely seriously” and makes clear to all its farmers and suppliers that exploitative child labor “will not be tolerated.”...