Stay in the Travelodge Southampton and park at BCP parking.
Have a look at the pre-cruise options here http://www.visit-southampton.co.uk/site/cruise-passenger-and-crew-information/pre-cruise-hotel-deals several users recommend the Holiday Inn and cheap, near to the docks and long stay car park - good luck.
Yes, we stayed at Holiday Inn next to the dock and had 15 days free parking but ask when you phone-Jo.
Which Holiday Inn is next to Southampton Docks.
Sorry, I only know we picked it from the internet as "Holiday Inn Southampton". I don't even know what the dock is called, but when we were there, Indie was moored next to the hotel, and the dock gate joined onto the car park, so we were a minute from the terminal wheeling the cases. Sea Princess was just behind, and we've travelled on P&O from the same dock. It wasn't the dock where QE2 left from which is further away. Someone from the area might tell you more? Hope it helps a little-Jo.