Ian, A good bet for running close to East Grinstead (EG) is Ashdown Forest (more heathland than forest) just a few miles to the south east of EG. As a previous poster mentioned the North Downs Way is not too far to the north, a good start point is Woldingham (a short hop on the train from EG) and then either east or west along the downs for an out-and-back run. In the general area there is a wealth of footpaths and bridleways but you'd need a 1:25k OS map to plan some good routes. The disused railway mentioned above is a good bet for a simple (surprisingly rural) run 'from the door'. Hope that helps.
Thanks all. Did a 6 mile loop pre breakfast on the hills near blackland farm around the bluebell railway, will go again tomorrow.