Is it realistic to take in both Salisbury and Stonehenge in a single day trip from London using public transportation to and from London and touring both locations independent of a commercial tour group?
Buy a Day Return Train ( earliest off peak) Ticket from London to Salisbury. Take Bus to Stonehenge. May need prepaid reservation time for entry. Return to Salisbury: Go see Cathedral and copy of Magna Carta. Take later pm return train. I did this myself except that I continued to Bath.
Yes. You will leave early in the morning from Waterloo railway station. Arrive in Salisbury. Walk from the train station to the old downtown area (several blocks). At the tourist information office, buy a ticket to ride the bus to Stonehenge and to enter Stonehenge itself. This ticket will also include Old Sarum, unless you tell her (the TI lady at the desk) that you do not want to see Old Sarum. The ticket is slightly cheaper then. Pick up a map of Salisbury at the TI.
Walk one block to the bus stop in front of the theatre/cinema.
The Stonehenge Bus will be clearly marked when it pulls up.
After touring Stonehenge, ride the bus back into town. Walk to Salisbury Cathedral and tour that.
Then have a look at The Salisbury Museum, across the lawn from the cathedral.
Walk a couple of blocks back into the center of town.
Enjoy the architecture and quirky streets.
Walk back to the train station; back to London.
EDIT: Wow Kathleen. We were typing at the same time (approximately)
I do love Salisbury!
Very doable, as described above. Better still, the hop-on-hop-off bus stops at Salisbury station, so you don't have to walk into the center to catch it. When you're ready to leave Salisbury, the station is a short walk from the cathedral or the center if you don't want to wait for the bus.
Or rent bikes in Salisbury and ride to Stonehenge as we did some years ago (1998).