They use different cars for different jobs, the basic police patrol car (panda car) is usually just something small like a Vauxhall Astra, Ford Fiesta or Ford Focus. For motorway policing and persuit they need fast cars so they use things like Volvo V70s, Vauxhall Omegas, and BMWs (3-series or 5-series). I think pursuit cars are modified for high performance, I've heard they can do up to 170mph because they take the limiters out of the engines. If the police have such fast cars, hopefully people will get the message that it is extremely difficult to escape the law. And sometimes they have 4x4s like Range Rovers and BMW X5s (God knows why they use this though). Regional police forces (each one usually covers a county or several small counties) don't all use the same makes of car, so you see more of a variety of different makes and models being used as police cars than you usually see in America (where the Crown Vic is King of police cars). Some forces even have a couple of souped-up Subaru Impreza WRXs. Maybe they choose BMWs because they are fast and nimble. And the Range Rover is a very good offroader. They also like to use estate cars (wagons) because they can carry more equipment. I don't know if they have any special deals with car companies, but with persuit vehicles they seem to buy the models with the most powerful engines and modify them even further. But they don't buy expensive cars for the "luxury", I don't think any police car has leather upholstery. One thing is for sure, British police work isn't exactly glamourous.

Years ago police used Jaguar MkIIs because it was one of the fastest saloons around at the time, it was also famous as a getaway car for professional crooks.

I'm don't know much about policing in Britain, but I wouldn't they say have better funding than America police. I really don't know. I don't know if we have more chases than in American but there are still plenty of them happening.