Why not use one of the taxi firms getting a quote upfront.. probably be around 100 pounds return

Or check the other recommendations on the Southampton forum - and search for "southampton" on the /London forum

I dont have an answer for you, just the same question. we are coming into London on the Aug.21st and cruising out of Southampton on the 22nd.

Sounds like hiring a private company maybe the easiest. Anyone else interested in renting a van or hiring transport to Southampton. All advise is welcom

If you can't find a reasonably priced private transfer you could consider taking a train from London Waterloo to Southampton. There are several trains per hour, journey times from 70 minutes. Return fares valid on any service after 0930hrs with no advance booking necessary are £33.20, return may be made on any day within 1 month. There will be taxis at Southampton Central to take you to the ship. Timetable: http://www.nationalrail.co.uk/