Getting from South Hampton cruise port to London City Center

Best in terms of what?
Scenery? Cost? Speed? Finishing point in London? Frequency of service?
Personally I would use the train.

Cost, efficiency, and easy to get to from dock, I suppose would be my top priorities.

Get yeself in a taxi to Southampton Central train station (less than a mile) and then take a train from there up to London. Note that some trains are considerably faster than others; it may be logical to not take the 1st one that passes through as that could be a seriously slow stopper. You may wish to refer to http://www.southwesttrains.co.uk for more info. I've used them with that much luggage before without any problems, although I'd avoid the tube with so much to lug around. Perhaps a hotel near Victoria would be convenient, failing that get a taxi on arrival in London.

Train is quite easily the best soloution, as you know what time you will dock book a fare in advance for the best price. Not sure if it is a typo but Southampton is one word.

Thanks fwoggie for the detailed explanation, and yes, richiavo- one word-thanks

National Express www.nationalexpress.com coaches from Southampton to London Victoria take about 140 minutes, run about once an hour and cost £7.00
Southwest Trains www.southwesttrains.co.uk trains from Southampton Central to London Waterloo take between 80 and 100 minutes, run three or four times per hour and cost £36.60 off peak or £39.20 anytime
Megabus www.megabus.com sells cheap tickets on underused Southwest Trains from Southampton Central to London Waterloo, there are only six a day Mon-Sat at 12:55, 13:55, 15:55, 17:55, 19:55 and 20:55 and none on Sunday, they take 100 minutes and cost between £20.00 and £6.00 or sometimes even £1.00 you cannot get the tickets more than about six weeks in advance and you are buying travel on a specific train unlike the Southwest Trains tickets which are more flexible but more expensive.

you can take a train or bus and then a taxi - i don't know the current fares but you can do a search and find the info.

Get yeself in a taxi to Southampton Central train station (less than a mile) and then take a train from there up to London. ... Perhaps a hotel near Victoria would be convenient, ....

The quick trains from Southampton arrive at Waterloo, not Victoria. There are occasional very slow trains from So'ton to Victoria, but they are very slow.

Or perhaps did you intend the OP to change at Clapham Junction for a connection to Victoria? Most but possibly not all trains from Soton to Waterloo will make a stop at Clapham Jct a few minutes before arriving at Waterloo, and there are connections to VIctoria every 5-10 mins taking about 7 mins. The ticket will probably be equally valid at both arrival points. Unlike Victoria, Waterloo isn't an area noted for the abundance of its hotel accommodation, though I expect there is some.

You'll find information more easily if you type in Southampton