Just checked in my game. The default config uses the arrow keys. To change this go to Driving Options, Controls, then click the second tab and edit the custom bindings.
Problem solved, but there's more to it than you described. I already knew how to do the bindings, I had simply forgotten there's certain functions you can't leave unbound.
If you just jump in there quick and rebind Accelerate, Left, Brake and Right to W,A,S,D, it leaves Shift Up unbound, because it's default binding is A. Why they would make you bind Shift Up when many using KB drive with Auto tranny, or why they would bind Shift Up to A by default when their default driving keys are the arrow keys is beyond me.
They need to understand that most KB gamers use W,A,S,D so much, their left hand is more dextrous than the right, at KB gaming anyway. They've got you driving with the right and and shifting with the left, which isn't even the way you'd do it in a real car if you're the typical right handed person.
I know CodeMasters is based in the UK and they have the steering wheel on the right in their cars, but this game is targeted much more toward US audiences than those in the past, just like DiRT. Anyway, like I said, problem solved. The only thing I'm having trouble with now is readjusting to the difficulty of GRID vs the NFS Undercover game I just finished, which is a cakewalk by comparison.