In reply to balmybaldwin:
All good points, particularly the weather. It can be surprisingly remote and bleak up there, even in summer and even more so in winter. In a storm you can almost imagine you are up on somewhere like the Carneddau - well, nearly
I've never cycled the whole route but have walked it, and agree that at times it gets a bit dull with hill after hill, but generally great views.
As for camping /bivying we took 4 nights and put the tent up late in the day and dropped it at dawn long after and before anyone else was around. Virtually anywhere out of the wind will do. Gorse bushes make good wind breaks, and as has been said there are lots of hollows and bumps to shelter in, and some flintstone walls and old barns to pitch behind.
I often do day walks along the Eastern sections between Chanctonbury Ring and Eastbourne.
I've known the Downs for the last 34 years and love them - it's the nearest we get to remote country here in the South East, and in winter Lewes holds the dubious record of having been the scene of the worst recorded fatal avalanche in Britain when a row of cottages was buried in the 18th century.