Transportation from Kensington hotel to Southampton for 6 people?

The easiest way would be door to door using a private transfer. The cost divided by 6 should be affordable. Second easiest would be the National Express coach. The driver puts your luggage in the hold for you. You would need taxis in London to the bus station and in Southampton to the docks (presumably the docks) so that adds to the cost. I leave the math to you.

Norma is spot on. We've found that using a car service based in the destination city works very well as they always seem to know the best way back home. Do a google search, email three or four telling them your needs and get some quotes. Prices can vary a good bit.

I can recommend a company based in Southampton which we used. West Quay Taxis are very responsive, polite and altogether a pleasure to work with. We used them as well to tour around the New Forest.

Norma and TC, thank you for your responses. I very much appreciate the information!