You ~could~ do this yourself. It's pretty easy and I'll tell you I'm not any kind of transportation whiz, lol! You can take the train from London Waterloo station to Salisbury. There is a local bus company that runs a shuttle out to the stones and picks up at the train station. It's called the Stonehenge Tour but it's not actually a tour in my book. There is a commentary out to the stones. You buy your ticket from the driver, they hop off at Stonehenge and buy the admission tickets, you head for the small land train shuttle out to the stones after you pick up your audio tour.
Coming back, get on the bus shuttle at the same spot. It stops at Old Sarum on the way back if you wish to get off, then returns to the City Center (if you want to look around) and train station. Get the train back to London.
Go to www.nationalrail.co.uk to check ticket prices. Buy your tickets ahead of time for cheaper prices.
There is also an occasional tour thru London Walks (www.walks.com) for Stonehenge but it might not be on the day you need it.
I would not recommend one of the combo bus tours from London that stops at Windsor, Stonehenge and Bath. Tries to cover too much territory and doesn't give you adequate time at any of the sights.
editing to add: Viator is not a tour operator. It's a 3rd party consolidator so if you want to do a tour you could figure out the actual tour company and book directly thru them. It might save you some money, it might save the tour operator some money.