In reply to oldie:
Yes, I did it about 15 years ago. It took us 4/5 hours. The most important thing is to get your tides right because there is NO ESCAPE apart from Birling Gap, so being cut off by the tide is a serious concern.
Keep well away from the bottom of the cliffs, they are very unstable, and chalk/stone fall is a constant threat. You'll need a long tide to be able to do this.
Then there is the constant threat of idiots throwing stones over the cliffs from above, I think if I did it again, I'd wear a helmet.
There have been some massive cliff falls in recent months, particularly to the section under Belle Tout where a huge section has collapsed. The sea is still stained white from this, and it looks as though there is more to follow. I walked up the steep path from Bedes School playing fields last week to the Bomber Command Memorial, and noticed that the sea below Beachy Head was stained white suggesting recent cliff fall.
Be careful scrambling on the boulders between the base of the cliffs and the light house at low tide, they are very slimy with sea weed and general green gunge. The thought of slipping and getting your foot stuck in a crack on a rising tide doesn't bear thinking about!
It's great fun and doable in calm weather on a low tide, but because of the increasing risk of cliff fall I think it's a lot more serious than when I did it.
There were quite a lot of wrecked cars from suicides along the foot of the cliffs then, rather sombre, but these may have been removed by now.
If you go for it, the Coast Guard ask if you would call them when you start and when you finish.