In reply to Martin Davies:
If it HAS to be the Downs, much of the north escarpment is open access but tbh I'm not sure it will be of much use to you. Newtimber Hill (East of Poynings) is ok but mostly farmland with grazing but you'd be better off at Wolstonbury just a little further East and right off the A23 for access. There are orienteering maps of much of the South Downs available online which are 1:10k so the small features show up better.
http://omaps.worldofo.com/?cid=113&s=&p=6
Maybe a donation to the club that mapped it but no way I can police that!
Devils Dyke is another option for open land, if I think of any more I might pop back.