Just to add to the echo in here, the car that caught fire was a 2015 Land Rover Range Rover Sport, with a diesel engine. The number plate has been read from one of the videos, and the MOT details looked up online.
It's obvious it was already on fire when it was driven into the car park, but the driver only realised once he was through the ticket barrier. He stopped the car in the middle of the driveway and some people (presumably including the driver) tried to tackle it with fire extinguishers but were unsuccessful and retreated.
A friend who knows Range Rovers suggested flammable material such as leaves getting caught under the vehicle where it's hot, overheating and setting off the catalytic converter. There's plenty to burn in a modern car, and once it gets hot enough the diesel in the tank overheats and the tank leaks or explodes, spraying hot diesel everywhere.