I would fly directly into Heathrow because for little money you purchase an all day pass to ride the tube (subway) from the airport to your hotel stop. There are tube maps in the subways so you know on which carrier to embark. We have stayed in the Kensington area and got off the tube right at the hotel street. You could go to tripadvisor.com and look for hotels there- most of the information concerning the hotelws will tell you which tube stop to disembark. To arrive in Harwich, I would take the tube to the train station and purchase a round trip ticket to the port area. Again, you may opt to overight in Harwich or arrive on the same day you embark. It is really very simple and we have planned and done our own arrangements many times. Have a wonderful trip.