"Don't mind long days, it's a once in a lifetime trip" is exactly my way of travelling, so here are my two cents.
For ENGLAND (moving around from and to London by train and underground):
Portsmouth Arsenal: HMS Victory and HMS Warrior.
London: HMS Belfast , Imperial War Museum.
Greenwich: SS Cutty Sark, naval Museum (oh, man, with NELSON´s uniform... ), Observatory.
Chatham Arsenal: The three ships: HMS cavalier, HMS Ocelot and HMS Gannet.
You should lodge at Bayeux, which is virtually in the middle of all beaches. You can start with the famous Bayeux Tapestry and, as an excelent introduction for the landings, the Normandy Memorial.
After this, from West to East:
Ste. Mére-le-Eglise: the village.
La Madelaine: Utah beach and Museum.
Point-du-Hoc: Battery and memorial.
Arromanches-les-Bains: Go up the cliffs on the left of the village to have a superb view of the Mulberry´s. Gold beach.
Courcelles-sur-mer: Juno Beach and the Canadian Memorial.
Berniéres: Juno beach.
Luc-sur-mer and Ouistreham: Sword beach.
Ranville: Pegasus Bridge and Pegaus Bridge museum (The bridge crossing the river is a copy of the WWII bridge, the original having been dismantled and reconstructed in the museum). Merville battery.
In case you have more time: Villers-Bocage (south of Bayeux) the place of the battle with Michael Wittmann.
If you have questions, or if you need more info, feel free to conatct me at: firstname.lastname@example.org