Codemasters glorious racing game
Codemasters' late 90s and 2000 spawn games were all in a class of their own. Having been involved with a lot of arcade games in the past they had developed a unique take on the ideas that the games they put out could conjure. Therefore, by the time this racer was put out, it the developers had already built a cool, well thought out combination of simulation and arcade that make this game thoroughly nice. Graphically it sure looks like it could have been developed later than it did, as it's just like a game that hadn't yet received the complimentary particle and graphical superimposed shower of glam rocking visual enhancements, but if you abstract these, (and I generally prefer playing games with bloom turned off) the basics are very modern and well thought out. As such, combine that well plotted physical simulation nd car handling that Codemasters were known for and you'll get exactly that great racer you were looking for. It doesn't have the over the top quality of games like Need for Speed Hot Pursuit
but it manages to create a great experience on its own terms.