Stonehenge is an obvious one and is on the way to Cornwall if you're going from Heathrow. The Cotswolds is another depending on if you're going that way.
I've been to the south of England a fair few times (Westward Ho!, Surrey, Cornwall, Isle of Wight and maybe a couple other places I can't remember right now) but can't think of much. Cornwall has a lot of character though, (when you are there make sure to try their pasties).
Depends what you're looking for, the scenery is great (there are quite a few 'areas of outstanding natural beauty' you could visit if you are into that thing -
http://en.wikipedia.org/wiki/Area_of...Natural_Beauty). Unknown Soldier and Tristesse will know their onions when it comes to down south.