The classically British automotive brands Jaguar and Land Rover had seen their fortunes soar under the stewardship of the Indian auto company Tata Motors.

But now that legacy is under threat.

Land Rover's market in China has been shrinking, Jaguar has a portfolio heavy on less-popular cars, and the fallout from Brexit threatens to raise prices on supplies Jaguar Land Rover uses to make vehicles.

Jaguar Land Rover's performance peaked in mid-2016, CIMB analyst Pramod Amthe told CNBC.

Since then, a slowdown in JLR's China market has been perhaps the biggest factor behind the company's woes. JLR has said its Chinese business is struggling due to challenging market conditions. But one report from Automotive News said the company was battling quality-control issues in the country.

"We feel the worst is nearly there in JLR performance," Amthe said. "Management efforts to cut costs and turn around have started yielding results in UK and USA. But China is taking longer than expected to revive."