Rolls Royce and Bentley still perceived as British brands and craftsmanship (no longer owned). They embody wealth, class system, quality.

What were once British Leyland marques - Austin, Morris, Jaguar, Rover Wolesley, Riley MG etc failed due to mostly poor management and obstructive out of touch unions. Some brands still owned overseas. What it says about the UK - low standards, inflated sense of importance, once world leaders who lost an empire.

Both are true in part and depending on your point of view, neither are very attractive perceptions. Cars are litte more than wheeled white goods with bling - they are valued as a way some can demonstrate visible status.

We should avoid linking cars to perceptions of the UK. Much the same as associating the USA with V8 motors - it may have appropriate 30 years ago. What do V8 motors mean today - two divergent views - (a) meaty, powerful, I'm in charge, or (b) inefficient, oil swilling, climate changing, overweight, I'm a dinosaur!

Way before multinational, homogeneous mass production, cars certainly tended to reflect national characteristics and a buyer of a Peugeot could be pretty sure that the car itself and most of its components came from factories in France (ditto VW - Germany, Fiat - Italy, BL - UK,...)
Back in the day when a car crashing over a pothole would produce the response "bad road!" from the British driver, but "bad car!" from the French, French cars were famed for soft, pliant seats/suspension, whereas German cars gave a firmer ride. Over time these two traits have moved slightly towards the middle, but the march of pointless bling among all marques has led to wafer-thin rubber and a rough ride for most cars three rungs up the price/specification hierarchy. (20" wheels as standard on a Scenic? What has the world come to?)
Small Fiats were great fun to drive, with foot to the floor to thrash them in every gear, but with arms akimbo owing to the archetypal Italian physique of long arms and short legs, common amongst the dominant Gracile Mediterranid ancestors who populated what are now car producing areas.