DRAX, England—Even as it faces increased regulatory scrutiny at home, America's dirty and unwanted coal is being embraced in one of the world's cleanest energy markets: the European Union.

At the biggest power plant in the U.K., operated by Drax Group PLC, a small black mountain of a million tons of coal sits at the base of a dozen 374-foot cooling towers.

Much of it is high-sulfur coal from under the plains of Illinois and...