Here are the UK sponsor codes for Burnout Paradise City that I have found so far, they work on PS3 and I am pretty sure if they are the same for Xbox 360, they probably are, maybe someone reading this can confirm.

Gamestop Car

B179 8M20 XA09 80FF

Steel Wheels Car

Z891 4K88 IN25 79AA

You will get the Gamestop car when you have your A Licence and Steel Wheels car you get that when you have your Burnout Licence.