LONDON—The U.K.'s antitrust watchdog Thursday said Ryanair Holdings PLC should reduce its 29.8% stake in Aer Lingus PLC because it is stifling competition on routes between the U.K. and Ireland.

The provisional ruling by the Competition Commission is the latest setback in the budget carrier's campaign to expand its operations in Dublin and other Irish cities. Ryanair, best known for its low fares for passengers willing to travel light, has taken advantage of cutbacks at other European national airlines and the collapse of...