A round trip in the British Isles. Two weeks, may be four.

We can more easily assist you if you tell us what sort of things you like to see and do.

I'm not a typical sort of traveler; I spend a lot of time walking around observing the architecture, and I like art museums and 20th-century-history museums. I'd want two days in York and more than one in Glasgow.

Many people who get as far north as Edinburgh and Glasgow want to see some of the beautiful Scottish countryside. A lot of the most dramatic scenery is in the western half of the country and on the islands, but there are interesting views all over.

You'll only scratch the surface with 4 weeks, especially if you include Scotland (and what about Wales?). You're going to get all sorts of suggestions, but some will probably not be aligned with your personal interests unless you give us some clues.

I'm open to anything, yet I do want to understand why the Scots want a division on their own. Were these issues always just awkward? For 300 years? I want to hear from the people and what they have to say if they want a Bresexit, from the Bresexit. I want to see the country side. I want to see the trains. I want to see how Europe made Mass Transportation work. I want to walk the walls of Edinburgh. I want to understand the myth that is Scotland, that I have carried in my head for most of my life.

Then you should spend more time than 3 days in Edinburgh with a daytrip to Glasgow. Spend at least a week, get out into the countryside, visit the site of the Battle of Culloden.

https://www.nts.org.uk/visit/places/culloden/the-battle-of-culloden

We found the Scots to be the friendliest people anywhere, so I am quite sure you will be able to talk to people. Or maybe take a tour that focuses on Scottish history—-from their point of view.

Your original plan was nothing like a grand tour of the “main island”, by which I assume you mean Great Britain. You’ve missed out the whole of south west England, the whole of Wales and most of Scotland.

There’s nothing wrong with that of course and the reality is that if you only have 4 weeks you will inevitably miss a lot out unless you turn the trip into a rally, which would be really silly.

"I want to see how Europe made Mass Transportation work"

The British may disagree with you on that, given their very expensive rail fares :)

And many of the British may disagree with this off repeated statement of expensive rail fares. That may be so for those who don't book ahead. But if you have the common sense and ability to book ahead there are lots of ludicrously cheap train fares.
Anyone under 30 or over 60 also qualifies for a railcard for 1/3 off. As do various groups of people between those ages.
Many other countries do not such reductions for locals to worldwide visitors, and why should they?

Given your answer you need to give a lot more time to travelling Scotland, and get a lot deeper and further into the Country. Do some reading into the history of the Jacobite movement, the history of religion in the Country, the Clan system, the Highland Clearances and the absentee lairds- all quite or even very complex subjects, and all of which inter twine to form modern day Scotland.
Culloden is but one small part of the Jacobite story.
The question of whether Scotland can economically become a truly independent and economically viable country is also an interesting one. You will not get a unified voice on many of those questions- for instance many in Shetland and Orkney would far rather join Norway (if the opportunity arose) than an independent Scotland, because that is where their heritage lies.

What are you really seeking in Scotland?- real heritage or some tourist board Romantic image with at best a shaky basis in reality. There is nothing really cuddly in the history of the Clans, which is often a savage and complex history. As brutal in many ways as the Clearances- some of which cleared villages you can visit by car or taxi, if not necessarily by train. Not something you often see people doing on this forum.

Re clearances. We explored the remains of "Field of the Springs" village out the back of Torridon. Apparently the village was cleared in the 19th century for use as sheep pasture.

Following up on isn31c’s excellent suggestions below are a few links to a couple of Future Learn’s free survey classes on Scotland’s history. These classes will give you a smattering of history. Also, I found John Prebble’s The Highland Clearances a great introduction on that topic.

We respectfully asked many questions similar to yours during our visit to Scotland. It was especially interesting to hear from Scots who voted against the independence referendum and their reasons for doing so. We found the Scots to be some of the kindest people ever encountered and seemed happy to find tourists actually interested in them as a people.

Links:
https://www.futurelearn.com/courses/the-highland-clans
https://www.futurelearn.com/courses/the-life-and-afterlife-of-mary-queen-of-scots
https://www.futurelearn.com/courses/battle-of-dunbar-1650

It appears they are no longer offering the class on the Jacobite Rebellion. Ther's always the possibility they'll bring it back at a later date.

"For some reason I can not figure out an itinerary."

To me, that means you may want to look at a tour.
(If you have 2 to 3 weeks)
The Rick Steves Scotland tour would be great:
https://www.ricksteves.com/tours/scotland/best-scotland-tour

Plus you would have an excellent guide to answer your questions about history and more.

You could fly in to Heathrow.
You could do several days in London, as you said, "then just being in town to fill out the other places we have never seen, or wish to revisit."
This time would include several day trips that you have named. (Dover & maybe Canterbury)

Then take the train north (up the East Coast line) to York; spend 2 to 3 nights.
Then travel on north to Scotland and join your tour.
When your tour is over, if you wish, you could travel south into England, paralleling the west coast.
Stop in Chester for a night or two, and anywhere else that appeals to you. (Liverpool? or Manchester?)

Return to London for a couple of nights.
Take the train to Windsor.
Spend a night or two there; see the castle.
Take a taxi to Heathrow (it's not far; a relatively cheap fare) and fly home.

I think you will see a lot this way and learn a lot from your Rick Steves guide.

Another alternative plan: (For four weeks, as you said in your headline)

Take a look at Rick Steves Best of England in 14 Days that includes Wales, the Lake District, Hadrian's Wall, York, and ends in London:
https://www.ricksteves.com/tours/england/best-england-tour
We took this tour in 2018 and loved it.

You could fly into Heathrow, take the coach (bus) directly to Bath to begin this tour.
The tour ends in London, with entrance fees paid to Westminster Abbey and Tower of London.

When this tour is over, take the train from London to Scotland and begin the Scotland tour I mentioned in my above post
You could then take the train back to England the way I outlined in my above post.
Or fly home out of Edinburgh.

The reason I've mentioned doing 2 Rick tours back to back is that I think this would give you the thorough understanding and experience you are looking for. Without you having to sweat bullets to plan it all.

Transportation and hotels are booked for you and many meals included.
There is free time on some days for you to find a lunch or dinner on your own.
Free time on some afternoons lets you wander as you wish without the group.
Sounds like a perfect plan to me for you, someone who says
"For some reason I can not figure out an itinerary."

Or take one of the Rick Steves Scotland tours, since your (the OP's) only comment in this thread seem to be about Scotland.

If you intend visiting a major city in the North West, I would opt for Liverpool over Manchester. The former is more of a tourist destination, lots of museums, two massive cathedrals and maritime attractions as well as the Beatles connection.
I live slap bang in between the two cities and consider myself more Manc than Scouse, but would say that Manchester is more of a working city, plenty to see and do but not quite as much as Liverpool. Oh and I consider Manchester to be the centre of the music world.
Liverpool has two rail links to Chester.

Liverpool and Manchester are very different but I think these days Manchester has at least as much to do for tourists and right now has an energy unsurpassed in the U.K., including London. Absolutely agree on music.

If you want to see public transit done right stay in London a bit longer. I personally prefer the upper level of city buses to the tube. It's my "do it yourself" tour bus with premium views. But the tube and rail system really does get you around quickly. The system is a little weak on step-free access, but light years ahead of Paris. If you really want to see best in class you could pop up to Portland (Oregon, USA). As for long distance train travel, Plymouth UK to Thurso UK (in Scotland) is about 759 miles and 16-18 hours. Pretty much biggest trip you could make on the "main island." It's about the same distance as Eugene, OR, to Bakersfield, CA, except ... nobody really wants to make that trip. That's the problem with long distance train travel in the US.

Plymouth to Thurso is actually just about 900 miles, and the rail system starts at Penzance, 80 miles west of Plymouth, so the longest journey is really all but 1,000 miles. You could not complete that journey in 18 hours. Northbound you would get stuck overnight at Inverness- more like 28 to 29 hours.

If you wish to learn about rail transit, then check out the following site:>https://www.seat61.com

Although the trains are generally very good in Britain, it is disappointing that the UK government have seen fit to cancel the northern legs of the HS2 high speed railway. So, we are going to be left with a high speed line from London to Birmingham and then back to the current tracks. for places north thereof. Others countries now have extensive high speed railways.

This You Tuber produces excellent videos on train travel:>https://www.youtube.com/@SuperalbsTravels

Francis, do you have any comments on what has been written here?

Usually the OP of a thread comes back to say "Thanks for all the suggestions." or to comment more about their plans.

Are you still planning a trip or have you forgotten about it?

Francis, I hope you come back onto this board and let us know what you actually decided to do. We are spending about 5 weeks on the great British island this summer and our plans are fluid. We'll have a car, so we don't need to plan too far ahead. But we know we'll spend some time in the Cotswolds, the Lake District, York, Glasgow, Dornoch and the northern Highlands, and Oxford. The exact itinerary we'll not really develop except the front and back ends in London.

Jphbucks - it sounds like you’re not planning to book accommodation ahead? When are you coming? If it’s any time in the Summer months then that could well be very challenging especially in rural areas. For the Highlands that probably applies all year round as many options will close in the off season.

You will probably find somewhere but it’s likely that you will be choosing from what’s left and you could be spending quite a bit of time every time you move looking for somewhere.

About planning ahead for accommodations, you may be onto something. I now plan to check AirBnB listings regularly leading up to our trip to make sure we're not locking ourselves out of all the good places. We're set for London at the beginning, but as of right now that's all we have. Maybe a good idea to get something lined up for Oxford near the end of our time in the UK.