We've currently got down that Carmageddon was released 30th June 1997. Not sure where I got this from, maybe IGN or Mobygames. The History page on Carmageddon.com agrees with us, but then they filled it with information from here.
Anyway, now CWA have found links to old versions of Carmageddon.com: circa 1996, 1997 and 1998, and you can choose different dates/pages... the site says "To Be Released 20th June 1997". So, i've fixed the date & am looking through those archives now!