I visited it a few years back. The best approach is from Birling Gap and it is advisable to contact the Coastguard before you go and when you get back as people get twitchy when they see people below the cliffs there. The cave is in full view of the lighthouse.
Coastguard control centre phone number was: 02392 552100
You will need to be a good climber as it is about 15 feet up the cliff (or take a ladder...)
It is a small tube, quite tight in parts with the occasional space where you can stand up (well, stoop anyway. I didn't get to the end because it was too tight
What Les said is all true about getting to the cave, be very aware of not only the tide but how rough it is too. Unlike Les I can't comment on the inside of the cave, as I wimped out on the climb up when I was there six years ago (I think this was after Les). The climb was sufficiently steep and difficult to make a fall a distinct possibility. I would seriously consider taking a builder's ladder of about 5m unless you have a good climber available! The photo below shows the entrances as they were in April 2006, things may have changed since then though...
Beachy Head cave is an eclectic taste! .....Les is absolutely spot on, as was Ed W.....it's tight and at best a wriggle with only a couple of places to turn around.
It has a few places where light enters the cave passage as over the years successive cliff fall has broken into the tube. This means that the fauna in the cave is prolific to say the least! So its good if you like Arachnids!!!!!!!
That being said though, it is quite interesting to do if but only the once!!!!!!!!!
The climb is a bit tricky as the chalk is quite slimy, I found some ice gear very helpful. Take three or four ice screws with you and some etriers, as you can aid up to it along with some old tat which you can thread to leave for an abseil out.
If you are in that neck of the woods and are interested, there is the Kent Underground Research Group along with the Wealden Lads. They are always doing things in the south east.
For info, anyone wishing to visit Beachy Head Cave can save themselves a long trek as it is currently blocked by a large rockfall. It is likely to remain blocked until at least next spring, and more likely several years until the debris is washed away. The cave will also be slightly shorter... Some determined digging could open up some alternative entrances a bit further west towards Birling Gap if anyone was really desperate.