April or September. Strict or loose schedule.

Welcome to the forum.

In Germany April can still have winter like conditions such as very cold temperatures, and also the opposite. A German saying is stating that month April is unpredictable: "Der April macht was er will" (April does what he wants to do). Also the naming "April-Wetter" (April weather) for days which have sun, clouds, rain or snow fast changing within hours.

September feels more like late summer but can have fresher temperatures in morning and evening hours. In this month a lot of events such as Oktoberfest in Munich or IFA fair and marathon in Berlin makes traveling to these cities more expensive.Southern Germany incl. Bavaria (Munich) often has rest of summer vacations in first weeks of September. A timing tip for Berlin is the end of August with the annual long night of museums which allow visiting museums up into night hours and sometimes with special events, e. g. a look into their archives.

Looking at your destinations you seem to have only larger cities in Germany as destinations and you would miss Northern Germany. I recommend to add something like Lübeck and/or Schwerin as a destination for 2-3 nights to add a cultural impression. Germany is not everywhere the same Germany: we have a lot of regional differences and manifold cultural offers.

It would help others to make meaningful recommendations by adding your interests or also dislikes.

Congrats on having a good length of time for your visit. It looks to be 28-35 days. Do your 4-5 weeks include your arrival and departure days? If so, deduct those days from your total time. You have listed 6 cities and 2 large areas (Normandy and Wales). Just counting the cities that leaves 4-6 days per city. Taking travel between locations you will use up a half day to a full day, depending on mode of travel, so deduct that time from your stays in cities. (Remember that changing locations involves more than length of a train ride or plane flight. There is time to check out of lodgings, get to the airfield or train station in good time, finding new lodgings in new location, getting there and checking in.)
Wales is really a separate country, and Normandy includes a very large area, but I imagine you are referring to the DDay sites when you mention Normandy. Perhaps you should narrow down your priorities for Wales and Normandy to make it easier to plan.

Back in 1974 my husband and I spent 4 months in Europe using our VW we picked up there and were able to travel on the fly, making no reservations ahead. We did it on the cheap and sometimes slept in the VW. Times unfortunately have changed and finding a place to stay without reservations is next to impossible. April and September, alas, don't seem to be shoulder season as much as they used to be. Not as bad as summer, but I fear flexibility even then is difficult, unless, perhaps you have a very high lodging budget and can go luxury.

My suggestion would be to be firmer in your plans/schedule. Not necessarily rigid, but lots more people travel in April and September than in the past. Also, do a little more thinking about what you want to see/do in the various locations so you can know how much time you may need there. Then you will know if you can get to all the places you mention, or if you have to pare things down. You don't want to spend a third of your trip moving from place to place, even if some transfers are only a half day.
Get a decent map of Europe or of the countries involved to see the big picture of how far apart the locations are, then check train sites (or The Man is Seat 61) to find out how long your move might take. Everywhere you want to go sounds wonderful to me. And it is doable to go to all of them, but I am not sure how enjoyable it would be for me. Remember, on a tour all the details and transfers are taken care of for you, a big timesaver. The forum here has many knowledgeable people who can answer your particular and general questions. Best of luck in your plans!

September is a better choice than April.

4 or 5 five weeks is great, but your planned itinerary takes in three places that are a considerable distance apart. Consider planning places closer together. Also, flying out of London will add $$$ to your flight, since the UK has a significant fee for flights out of the UK.

If you still want to do this, fly into London, then Normandy, then Germany.

Most or your trip is in Germany. We lived in Augsburg, 50 miles west of Munich and have done all the places you listed.

1) Germany- You need at least 5 days in Berlin, then a day or two in Dresden. Bavaria is special, you could easily spend two weeks just there. Yes, Munich for 3/4 days, also consider a day in Nuremberg (on your way from Dresden to Munich). After Munich head to Salzburg/Berchtesgaden for 3/4 days, then consider Vienna for 3 days (I know it not in Bavaria, but Austria). Then head to Garmisch/Fussen, do the Zugspitze (highest. mountain in Germany). Take the cable car or cog train. Do visit two of King Ludwig's castles in the area, then take The Romantic Road up through Augsburg (2000 year old city), visit several medieval walled villages, most notably Rothenburg ob der. Tauber.
https://www.romanticroadgermany.com
The road ends in Wurzburg.

2) Normandy is great, visit Bayeux and the D-Day beaches and American Cemetery. There are other sites like Mt. St. Michel that are on the border with Brittany that is a great site. You may or may not have time to see it. Your need 2/3 days in Normandy.

3) London, Wales and Liverpool- Glad you mentioned Wales, it is special. My paternal ancestors came from South Wales in 1716. We visited the village where they came from in 2017, North Wales is close to Liverpool and is a great visit. Do visit Conwy, it is a large medieval castle that is interesting. Also, there is some very scenic area in North Wales, do some research and decide what to visit. You many wish to visit Chester, an ancient Roman city, near Liverpool. You must be a Beatles Fan, there is plenty of Beatles stuff there.
Consider visiting some small cities and town that are in SW England. Stratford Upon Avon is great, especially if you are a Shakespeare fan. Bath, Oxford, Stonehenge, Salisbury and Winchester are great. Also, Canterbury SE of London. If you really had more time York, north of London is my favorite city in England.

I suggest that you plan you lodging and transport for every day and stick to it. In my younger days, we did travel on our own with no fixed schedule and suffered because we arrive at places where NO lodging was available. One night we had to stay in a hotel's room where their workers slept (the Hotel had mercy on us).

Don't plan on having a rental car in a large city like London or Liverpool. Don't even think of driving into London. If you arrive in London, take a bus or train to a city like Bath or Oxford and rent a car (have your rental car booked if. you do choose to rent). Driving on the left can be a little confusing, my wife kept telling me to "stay on the left."

You need a minimum of two weeks to do what. you planned in the UK.

"...you seem to have only larger cities in Germany as destinations..."

For this reason, I assume your travel will be largely by train... Normandy may require a car if you are visiting D-Day beaches, as many do.

True about the absence of small towns. Maybe your '25 guided tour took you to smaller places in Germany, but if not, it's an easy fix in '26. The Berlin > Dresden > Munich train route offers stops in Erfurt and Bamberg. Both are medieval-town standouts with UNESCO World Heritage designations, both worthy of inclusion. A night or two in one or both would be time well spent.

I would book places that suited me in advance. I don't like "leftovers" or wasting time trying to find them.

Deutsche Bahn journey planner and booking platform for train travels in / from / to Germany: https://int.bahn.de/en

Thanks to all that have replied. Those are some great ideas and tips.
We'll have make some decisions and perhaps a few changes but it's all great info.

Geovagriffith, my ancestry is also from Wales so I thought it would be a good opportunity to visit.

Thanks again all!