There are quite a few threads on here about it. Check out the South Downs Double site for gpx files and tap info. http://www.southdownsdouble.net/
You really want good weather or it would be a slippery chalk/mud fest. Avoid the BHF weekend unless you want to share the trail with hundredds of others.
It's a good ride, logistics for getting back to the start can be tricky. I just take enough bars/gels/soreen for 10 hours, sorted. Have loose plans to do it sometime this summer, but this time riding from home so it will be Swindon to Eastbourne via Winchester, should be about 150 miles.
Good luck and enjoy!