SAMLESBURY, U.K.—After more than a decade in which building Eurofighter Typhoon jet fighters has been the backbone of BAE Systems PLC’s combat aircraft production, the defense company is shifting its focus to the new F-35 Joint Strike Fighter and what may come next.

BAE Systems expects sales from the Lockheed Martin Corp. -led F-35 program to jump in coming years as its work on the program surpasses production of the Typhoon combat jet, Chris Boardman, managing director of the British arms maker’s military air and information systems unit, said.

With its role on the F-35 limited to being a key supplier, the British weapons maker also is trying to retain its ability to lead future combat aircraft developments to remain a top-tier military plane maker.

BAE is working with other U.K. and French firms to develop a stealthy combat drone that could surveil and strike ground targets. A small group of engineers also is exploring what a future air-superiority combat plane might look like, Mr. Boardman said, though fielding such a system may take another two decades. BAE also is supporting Turkey’s indigenous combat aircraft development program called TFX.

The Franco-British combat drone program, through which both countries hope to keep up with more advanced U.S. developments, received a boost in March when U.K. Prime Minister David Cameron and French President François Hollande pledged €2 billion ($2.3 billion) to develop a drone to fly around 2025 and potentially enter production a few years later. “It is the most advanced program of its kind,” Martin Rowe-Willcocks, head of for future programs at the BAE Systems unit, told reporters.