Stonehenge is not in London, so I can only assume you are visiting from another country?
It's about a two hour drive, doesn't have good transport links, and while it and the visitor centre are interesting, I wouldn't go there if I was visiting London as you'll miss a lot of what the area has to offer. If you are only in London for a couple of days, why not concentrate on that because there is so much in London. A four hour drive for a bunch of stones is a harder sell.
Make a dedicated trip towards the south west on a second occasion and you won't regret it.
Stonehenge, Salisbury Cathedral, carry on in that direction and you'll have Bath, Glastonbury, Wookey Hole, further still and you'll have Lyme Regis, then Dartmore and Dartmouth. Amazing places that deserve a full day each.