You've got two convenient options for most journeys to or from the port when you're off on a cruise vacation from Southampton.
Private transfer is the most convenient, although care should be taken that traffic around London can add a bit of time to the journey. Expect a little over 2 hours via the M3.
Train journeys are a fantastic way to see the countryside and to get around the UK without the worry of traffic, although delays do occur on the tracks from time to time.
Departing from London's Waterloo or Paddington stations, expect about an hour and a half to two and a half hours. The Waterloo option has the least likelihood of a change, but both routes offer regular departures throughout most days of the year.
You will still need a taxi to complete the journey from the train station in Southampton to the port terminals area.