-London-Paris-Normandy(best travel itinerary) in May/June timeframe

You say "I don't want to rent a car", but, unfortunately to tour Normandy it is difficult without a car. Most of the D-Day places are rural, no good public transport.
You say "maybe get a driver", that would not be cheap (too rich for my budget!).

Now a radical suggestion. Take a ferry from Portsmouth to Le Havre, Caen or Cherbourg. Ferry company website here: http://www.brittany-ferries.co.uk/ferry-routes/ferries-france/portsmouth-france
You are then duplicating the D-Day route, and avoid doubling back via Paris. Portsmouth is an easy train ride from London (and has things to see). At Le Havre, Caen or Cherbourg you can pick up a hire car (or expensive car + driver), and after a few days get a train to Paris.

Thank you for your quick response,- will investigate the route you suggested and Portsmouth to LeHavre. What are the distances between Caen, Rouen and Honfleur--appears we would have to arrange for car service if not renting a car

Thanks again

You can get estimated driving times (tending to be optimistic), distances and routes from viamichelin.com. Check rail service within France on sncf.com.

All the places you have mentioned are served by trains or buses. I traveled through Normandy that way myself in July. I found that Bayeux was a good place from which to pick up a one-day van tour of D-Day sites. I used Overlord Tours but there are other options. A tour will be a much better use of your time than trying to get to the sites yourself, even if you do have a car. The tour drivers/guides know exactly where they are going and can provide a lot of information. Bayeux also has a good D-Day museum on the edge of town, walkable from the center if you aren't in a hurry.

Except for D-Day sites, Caen is a better base or moving around by public transportation. It has a huge Peace Museum that covers the lead-up to the war, the Normandy invasion, and the Cold War. The museum is well out of the center of town, but there is a public bus that will take you there. Check the schedule in advance, especially if you're thinking of hitting the museum on Sunday.

Caen has a few important historic buildings but was pretty well flattened during the war so is not as picturesque as many other cities in France (including Rouen). Rouen, too, was hit hard, but much of the historic center has been restored/reconstructed in the old style.

This is quite helpful! Thanks again for your suggestions, will check out distances and staying in Caen as suggested as possibly a base.!

Be aware that the ferries don't run every day from every port. There are periods when some of the boats are in for maintenance, in addition to the routine schedule rotation. We did the reverse of your plan, starting in France, and booked an overnight ferry from Caen to Portsmouth -- BUT it was canceled on just a few hours' notice due to a labor dispute (they didn't tell us why but we found this out later). We had to race to Cherbourg and leave our rental car in the parking lot at Cherbourg port in order to get to England, and our landing port was Poole, not Portsmouth.

Not that this is likely to happen to you, but just be aware of the need to be flexible!

Once you are in Cherbourg or Caen or Le Havre, you can connect with any of many bus or van tours of the Normandy coastline. That will be less expensive than hiring a private driver and will allow you to see most of the popular sights. Rick Steves cautions that some of these tours are better than others, so check out the customer reviews before you choose one.

Our time was allocated differently, but we made a very similar trip in 2015. Flew into London, stayed in the Victoria Station area three days, took the Eurostar to Paris for a week, then did Normandy as a day trip by rail. You definitely don't need or want a car in London or Paris. I'd second the recommendations for one of the D-Day tours in Normandy. We did a whirwind half-day and were glad we did it. I'd love to have several days, as you plan. Many people recommend Overlord tours, though they were booked full when we were there.

We didn't spend any time in Caen, but we found Bayeux to be a lovely town in our brief visit. At least stroll around for a few hours, visit the cathedral and definitely see the Bayeux Tapestry, telling the story of the Battle of Hastings in 1066. It's one of the most well-presented, informative museum displays I've ever seen.

You might find Rome2rio.com useful in scoping alternatives to get places. The ferry might be fun, though probably take longer than the trains between London and Normandy. You would sort of duplicate the D-Day route, with the very important difference that no one will be shooting at you when you land. ;-)

Overlord or one of the other guided D-Day tours from Bayeux or elsewhere would be a good idea. The Memorial de Caen (Peace Museum another poster referred to) is a great experience -- the WWII part better done and more interesting (to me at least) than the Cold War part. And the Bayeux Tapestry, very thoughtfully displayed and explained, is not to be missed, also the nearby Norman cathedral. Bayeux also has a WWII museum which others have recommended on this board. I believe it focuses mostly on the Normandy invasion and aftermath, while the one in Caen deals with the war as a whole.

Lacking a car will certainly complicate your Normandy experience, but it should be doable if you don't try to see too much. Rouen might be a good stopover on the way back to Paris, either overnight or for most of a day.

EDIT -- You've probably already considered this, but the days around June 6 will be busy in Normandy and there will be more visitors, fewer last-minute hotel rooms, etc.

This summer I had the same ferry problem as epltd, but in reverse. I visited first Normandy, then Jersey in the Channel Islands. I was heading to Poole on my way to Cornwall, but the ferry was canceled three days in a row, reportedly due to weather. I ended up getting a not-too-expensive last-minute ticket on EasyJet to London-Luton and taking two buses to reach my non-refundable hotel room in Poole. It could have been an even costlier experience. My first trip to the Channel Islands back in the 1970s or early 1980s also included a canceled ferry.

Perhaps the direct ferries between England and France use different equipment and are less subject to cancellations. I do not know. But I highly recommend that you have a back-up plan. If the thought of a ferry cancellation makes you quake because of a tight schedule, I recommend altering your routing and taking the Eurostar under the Channel or flying instead.

We have a very similar trip approaching.

Wed: Arrive early morning after o/n flight; make our best effort to stay up all day
Thurs: London
Fri: London
Saturday: London
Sunday: Paris via Eurostar; arriving early enough to tour the rest of the day
Monday: Full Normandy day tour with Overlord Tours
Tuesday: Reims
Wednesday: touring in the morning/afternoon; return to London in the evening
Thursday: London (and Hamilton that night!!)
Friday: London
Saturday: Flight home

I would like to take a day trip out of London, but I have been to Bath, Stratford Upon Avon and Stonehenge and felt they are a bit "eh". I love history and such, but I need to "touch" it. This is my husband's first trip to London and Paris and he is also an amateur photographer. Suggestions are welcome.

Caen as a base for Normandy make sense. It has more hotels and restaurants, its own WW2 history, a "peace" museum that is well regarded and runs tours to the invasion beaches, plus the fortress castle of William the Conqueror. Or Bayeux is a quick train ride away. Please consider spending the money to do a guided day trip for the invasion; you are paying for the guide's expertise which will make it a far more illuminating experience than going on your own. Some tours operate to other parts of Normandy.
Portsmouth, on the other side of the channel, is well worth a day on its own if you are interested in things nautical. Its harbor is guarded by a formidable castle which has guided tours. The huge navy base is a prime attraction for exploring Imperial Britain's seaborne history. Lord Nelson's flagship, the Victory, has been painstakingly restored and offers an illuminating audio guide for touring (but not cheap, and the security at this major naval base is tight.)
https://www.visitportsmouth.co.uk/
http://www.caen-tourisme.fr/en

Elzregina, if you haven't already done so, I suggest starting your own thread to ask about day-trips out of London. That way, your question will be noticed.