Hi oriema2002, have you considered transferring from Southampton to Salisbury for an overnight stay to explore that city as well?
You could then leave your luggage at the hotel and see Stonehenge in comfort.
For travelling from Salisbury to Edinburgh, as you thought you can avoid London, by taking a direct train to Bristol (Templmeads) in 1h30m. From there, trains run direct to Edinburgh every hour - but don't expect them to be cheap :o(
Another option which might be worth looking into is having visited Stonhenge, travelling back to Southampton Airport & catch a FlyBe (reasonable budget airline) flight to Edinburgh, they fly 4 times a day & take 1h30m. They will charge you extra for your luggage, but well worth a look.
If you need more details on these, or decide you want to find a taxi/private hire, then drop another line on the thread & we'll try & make some suggestions & get costs.
Have a great crossing,
Last: Oceania Nautica Aug 2016
Next: Cruise Maritime Magellan Nov 2016
Then: P&O Oceana December 2016
Golden, Grand(2), Caribbean, Royal, Sea(4+1 aborted)
Adonia(4+2), Arcadia, Artemis(2), Aurora(5), Azura(2), Britannia, Oceana(3), Oriana(12), Ventura(2), Victoria(5)
QM2(2), QE2(9), QV(7), QE, Caronia(2),
Oceania Nautica, Minerva, Minerva II, Fred.Olsen(8), NCL Jade, =X= Eclipse, HAL Ryndam, Aza.Journey