I suppose you could just do it in a long day, starting as early as possible.

Stonehenge opens at 0930, so you'd need to get the 0710, or at a pinch the 0740 from Waterloo to Salisbury (the train takes 1hr30). If you got back to Salisbury for the 1220, you could get back to Waterloo in time to get a train out to Hampton Court to arrive for about 2-2.30. Hampton Court closes at 6.

(You could try changing at Clapham Junction, but I think Waterloo would be easier). I don't know of any direct transport between the two, but it couldn't possibly be faster than the train.

Those amounts of time seem about enough to get at least some experience of each place, depending on how much you want to linger at Stonehenge (personally I think one needs to go into the surrounding landscape to see how people would have approached it from a distance, which adds an atmosphere that you don't entirely get if you stick to just plodding round the stones with everyone else: cross the road - if you dare - to go up the hill behind Stonehenge and look back, and you will see the stones magically disappearing and reappearing in the folds of land).

Get your tickets in advance, of course.

"What would be the best way to visit both these places in one day?"

Sorry, but there isn't one. Even driving yourself in a rental car it would be awfully difficult. Pick one of them and save the other for another trip . . .

Forgot to give you the link
www.nationalrail.co.uk

You should be able to order tickets online and then pick them up at Waterloo (make sure you use the credit card you ordered them with, and it's probably advisable to pick them up the day beforehand rather than risk problems when you're racing for a train).

Patrick gave you the "possibility" -- but in real lifeI don't think it would work.

Unless you want to spend hours on the train (more than actually seeing the places themselves)

The bus from Salisbury to Stonehenge (and return) only runs on an hourly schedule so that could mess up the best of plans.

I knew there'd be a weak link somewhere.

Well...that's disappointing. I completely forgot about the most basic thing which is closing times. I just assumed Hampton Court would be open until later. I really, really want to visit Hampton Court. More than I want to visit Stonehenge to be completely honest. Problem is that my friends all want to go to Stonehenge more. I can definitely do it by myself, that's not the problem. You all seem to have been to both places or at least one, which one did you like best? I know this depends completely on me and what I want to do, but I still would like to know how many people recommend each place.

Patrick thank you for trying! Haha, but yes, you're right it would be too tight. Especially since I'm the kind to walk around slowly, looking up and down, and see everything from every angle and be absolutely the slowest person in the world. Drives most of my friends nutters.

Why don't you go to Hampton court and let your friends go to Stonehenge? They are so completely different it will be difficult for anyone to really help you decide...

I think that's what I'm going to do. I know, it is a silly question to even ask. I was curious as to people's opinions on both of them though. And I think Hampton Court is closer to London so I would also have time to sight-see a bit and maybe go into either the Tower of London or Westminster. I've been to both, but have not actually gone inside. They tell me they're both pretty spectacular so yeah.

"Problem is that my friends all want to go to Stonehenge more. I can definitely do it by myself, that's not the problem. You all seem to have been to both places or at least one, which one did you like best?"

Totally apples and oranges.If you are just talking about the stones vs. the palace . . . Then Hampton Court Palace hands down.

But Salisbury and the cathedral are really very nice. So Salisbury+Stonehenge makes a really good most-of-a-day trip.

If I were you though, I'd send my friends off on the train to Salisbury, and go to HCP on my own and either take the boat back into town (if the weather is nice), or plan on something else in London for the late afternoon.

That way everyone can have their heart's desire

we were posting at the same time . . .

Haven't been in the Tower of London? Then definitely combine that with HC for a long but terrific day!

(Your friends will miss something terrific, but I do understand their desire to see Stonehenge, so their adventure to Salisbury/Stonehenge will be memorable for them, too.--But definitely The Tower for you!)

"the Tower of London or Westminster. I've been to both, but have not actually gone inside"

Then you haven't actually 'seen' either one of them. That is like saying I've been outside the British Museum but never been inside.

You have lots of options- but HCP and the Tower is a really difficult pairing. Each is about a 1/2 day's worth and take about an hour to travel from one to the other (90 mins including walking/wait time). You'll be lucky to get to Tower Hill by 3:30PM and it closes @5:30.

Why not Westminster + the Tower instead?