Those would have been my next questions. I wonder if shuttles are available?
England's major cruise ports (Portsmouth, Southampton, Dover, and Harwich) are a ways from London, so a shuttle or a taxi would be pretty expensive. You probably will save money by booking trasnfers through your cruise line unless you have a large party travelling together.
We used the train from Dover to London and there isn't any baggage handling , you do it yourself. It's a commuter train and you keep your luggage with you. Not really a problem and an interestig ride.
Living locally to the Dover Cruise Terminal another method of transport springs to mind. If you would like to include a quick trip to Paris on your cruise trip,after the Paris part of your journey, catch the the Eurostar fast train from the Gare du Nord in Paris to Asford in Kent. That is then only a good taxi ride to Dover or some of the cruise lines do collect from Ashford. You would then also get to transit the Channel Tunnel as an additional part of your itinerary.
Last year we landed in Gatwick at 8am---4 hours before the Celebrity buses were to pick up the passengers and take them to Dover.
My hubby decided to rent a car at the airport. It only took 1 and a half hours all freeway to drive to Dover. We dropped the car off 3/4 miles from the dock at the car agency (no extra charge), and they had a taxi waiting to take us the short distance to the ship.
It was not very expensive, and much more convenient. You also have the opportunity to drive around Dover if you get there early enough before the ship embarks.
We will probably do that again on July 29 on our Constellation cruise. It is much easier, though, to take the Celebrity bus transportation back to the airport----it is continuous and convenient!
Just read your post...hope this answer gets to you in time....Several years ago, we went from London to Dover via train...It took about 1 hr and a half and was very interesting to see the countryside (farm, etc) ... I'm sure you could reverse the trip and then once in London transportation to the airport is easy...
We took a cab from the ship to the bus depot (which was down the street).From there we took the bus to Victoria Coach (senior rates). When we arrived at Victoria Coach, we met fellow pax who took the transfers and arrived at the same time as we did....at a fraction of the cost!