Couple of things to consider:
There are a lot of military exercises on the Plain and red flags indicating no go areas. You can drift into them very easily and get in big trouble (or killed by bombs!!). Check out this link for info on activities
http://www.collingbourne-ducis.com/SPTA/index.htmlPeople do park here without any problems:
http://www.streetmap.co.uk/map.srf?x=41 ... 53695&lm=0You can drive up the yellow road which turns into a byway no problem - it is tarmac.
Where are you based? You might benefit from joining the TRF as many groups go to the Plain and you can get a guided tour, then record the route.