LONDON—Activist investor ValueAct Capital Management LP doubled-down on its big bet on Rolls-Royce Holdings PLC as its stake in the British engine maker topped 10%.

ValueAct crossed the 10% reporting threshold on Nov. 18, Rolls-Royce said Thursday in a regulatory announcement. ValueAct, Rolls-Royce’s largest investor, reached the new shareholder level a week after the company issued another profit warning that caused shares to slump.

The...