As the tranfer to Southampton is included, you probably will be first kept at the airport or a nearby hotel to make sure you will not arrive too early, and than directly taken to the cruise terminal in time to check in and board.
But if you really have time in Southampton, there is plenty to see. A good start for a cruise is the maritime museum with a lot of displays and artifacts from the Titanic and many other ships of the past.
If you like an extended walk you can follow the Titanic trail which leads to several Titanic memorials. Southampton lost several hundreds live in those tragedy.
More interested in more distant history? Walk the medieval walls or visit the medieval merchants home.
Enjoy Southampton and your cruise!
I would imagine that Cunard will handle your luggage from the time you check in at the airport or arrive at Heathrow. When I have used Cunard transfers to get to Southampton, Cunard took over my luggage as soon as I checked in someplace. I never had to carry my luggage with me once I was in Cunard's hands.
You won't have time to flit off once the bus drops you at the terminal in Southampton since the terminal is a long way from the town center and to be honest there isn't much to do in Southampton except to go to a pub or two. You would be better off taking the tube to London center after checking in your bags in a baggage hold area at the airport (Heathrow) and flit about in London. But that could be time constraints as well so plan accordingly.
to be honest there isn't much to do in Southampton except to go to a pub or two
unless of course you want to, as previously suggested by lfinfo, take in the Medieval walls, Titanic Trail, visit the Cunard 175 Exhibition, visit the Bargate Museum, the Art foundations, the Maritime Museum, or Aviation Halls.
Then of course there are plenty of shopping & coffee house opportunities, all within easy walking distance of 3 or the for terminals in Southampton.
But having said all that, most lines will stop off on the Motorway for a comfort break thereby making sure that you arrive early to mid-afternoon to be able to check in & board the vessel straight away.
Hope you have a fantastic time,
Last Cruise: Royal Princess August 2015
Next: P&O Oriana October 2015
Then: Queen Victoria January 2016
Your plans are obviously already set, but if you get to do it again I'd strongly suggest that you not fly in and cruise out on the same day. The jet lag, the bus ride down the motorway, the hubbub of checking in (even if it goes smoothly) all conspire to make it a pretty "full" day. I don't know your itinerary, but if it's just a crossing, naturally it doesn't matter too much because you can sleep as much as you want and just pretty much do what you want for the week. But if you're doing ports for the first two days you could find yourself walking into walls after a jaunt like that.
A few weeks ago we came back on the QM 2 after a wedding in Winchester, which is just north of Southampton. We stayed at the Southampton Hilton for five nights and made it our base of operations for the wedding, sundry parties and other enjoyments, including Salisbury Cathedral and its pretty interesting Magna Carta exhibition. On previous sailings from Southampton we've also arrived early and driven to really neat places like the New Forest, Portsmouth, and the like.
We think it's always a good idea to arrive at a cruise port at least a day or two early. . .for international itineraries that involve jet lag, we consider it a must.
In your situation, with a cruise line transfer from LHR or LGW, as others have said, there's really not much you can do as a practical matter except ride the bus and get on the ship. You don't have time for anything else, and as others have said, the dock isn't at the city center.
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