I don't think so, common ground is for the use of the 'common folk' and I think grazing horses are the only form of transport allowed. There is a law dating back to the Magna Carta (possibly even before that) which still stands as far as common ground is concerned and although cars obviously aren't mentioned I think the rights of those allowed to use the ground are still binding so as cars aren't mentioned, they're not allowed. I could be completely wrong - someone will correct me very soon if I am, but a little part of my O'Level History brain is telling me this!!