The only game I know exactly like that was Turbo Esprit for the Spectrum 48k.
The extremely weak plot was that you had to catch drug dealers by bashing in
their cars with your lotus.
But it was great just going over red lights and mowing down pedestrians. You
even had proper garages to stop for fuel, indicators, dead ends, 3 point turns,
4 different huge city maps, roadworks to avoid, men up ladders...
Surely due for an update !
Jeff