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.