As I kid in the UK I heard the same stories, is this still a thing? For the last few years I've been living in Lithuania which has a very big used car parts market, but I've never heard of cars being stolen and chopped up.

Usually parts are sourced from crashed cars, which are bought by breakers who often specialise in a specific model, and resold on online marketplaces. They don't present any form of 'verification' so I don't see why it couldn't be used for stolen parts, but it seems that it isn't.

I have heard about people breaking into BMWs and stealing the media console, but as I understand thefts of the whole car or even easily accessible body parts like wheels are very rare.

I don't feel that it is that security has changed much - if it is organized crime then it's no issue to get a car carrier with a crane and lift the car away. Maybe people have just gotten better morals since the 90s?