The answer to the question is difficult because it depends on some definitions:
What do you understand under a "GP car"? A car intentionally designed for GP races or a car that the owner realized did somehow comply with the then current GP rules?
What do you understand under a "street car"? A car built for everyday´s use in open traffic or a car that was intended as a competition car, but where the rules required that it must have been "street legal"?
What do you understand under "based on a street car chassis"? Does it mean it uses some tubes of a street car or must the complete chassis be unchanged, including suspension, brakes etc.?
Finally, what do you understand under a "GP"? An event for the Driver World Championship or any event carrying the term "GP" in the title? (Like some of the French GP were sports car events)
For example in the US GP 1959 at the back of the grid there was a Porsche Spyder driven by Harry Blanchard.
Maybe not exactly what we would understand as "street car", also I think it was modified to central mounted steering wheel, but otherweise quite similar to cars used in open public. Also I think the Porsche 718 monopostos were very much based on the same chassis, but of course they had originally been designed according to Formula 2 rules which happened to become Formula 1 in 1961...
Besides that, immediately after the war there were quite a number of "stripped" street cars (or street car chassis with changed bodywork) in GP racing. For examples the Delahayes, Delages, Talbots. And lots of specials were composed from parts of all kinds of street cars.
Edited by uechtel, 18 July 2014 - 09:45.