Southampton is the busiest cruise port in the country, with multiple terminals used by different cruise lines, so confirming exactly which one your sailing departs from is worth doing before you travel — a driver briefed on the right terminal avoids any last-minute confusion in what can be a very busy embarkation area on peak sailing days. The M3 is the main route from London, at its busiest with weekday commuter traffic, so an embarkation day falling on a weekday morning is where a little extra time in the schedule helps most.
Because Southampton departures are often week-long or longer cruises, luggage tends to be heavier than for a typical trip — frequently a full case per passenger, sometimes more for longer voyages — so confirming your group size and luggage at booking means an estate, MPV or 8-seater is arranged from the outset rather than a saloon proving too small when you arrive at the terminal.
With multiple ships often departing on the same day, terminal areas can get busy in the hours before a popular sailing, so building in extra time beyond the cruise line's stated check-in window is a sensible precaution rather than cutting it fine.