I've taken so long to post, it looks like some of this may already be covered...
One of the best pieces of advice I heard (maybe from Rick Steves originally?) is to believe you will return to a location again so you're not distressed at what you can't do. Usually once I've spent time in a place, I decide there's much more I want to do.
Our family (and also just my husband and I) have had some vacations in which we've really moved quickly from city to city. That strategy was right for those particular trips, but not always ideal.
Just before our eldest was entering his senior year of high school (in April or May my husband and I: "Omg, this is our last guaranteed summer"), we did a whirlwind trip (not in this order) including London (definitely limited--included the Eye, the Tower, Trafalgar Sq, a Globe show, British Museum, another museum or two? and ??), Cornwall, Bath, York, Cotswolds, Edinburgh (Fringe Festival/Tattoo/R. Mile). We went up to Culloden/Inverness for a day & so we'd have a longer night train back to London. Oh, we also did a bus tour of Oxford, had about half a day at Warwick Castle a day in Wales (Caerphilly Castle; husband says also Rhymney and Newport, but I don't recall). I'm tired realizing how much we did.
We broke all the rules about stuffing itineraries, but we had rail passes and just hopped on the trains with our backpacks. I think Oxford and Cardiff were last minute impulsive day adds.
I don't recall that we had done much planning in advance aside from accommodations and car rental:
York (1 or 2 nights), Edinburgh (2 nights), Cornwall (2 nights?) Moreton--in-Marsh (Cotswolds, 1 night). Bath (day trip), and our London B & B (maybe 2 nights?). We also stayed near Reading at a college I had attended a quarter century before :). I think we were there at least 3 nights, so we used it as a base for both London and afield. Our total trip was about 2 weeks. Would not recommend two of our nights--the night trip from Scotland trying to sleep in our seats (kids slept fine!) and our last night at the airport. We stayed in London until about midnight then headed to the airport to attempt 4 hours of sleep. We had a very early flight home to Seattle.
We were fortunate that we found rooms at BnBs from Rick Steve's England. Now, one can't count on booking rooms so late in the spring for an August trip for a family of 5.
The Cornwall days were to visit a couple of my ancestral locations. We travelled by train except in Cornwall where we really needed the flexibility to visit the locations. I also visited a records office with whom I'd communicated. Even though it was a brief visit in Corwall, our churchyard visit for looking/finding ancestors' graves was a great prologue to our only other full family vacation since-- fall 2022 with our adult kids when we showed them a German graveyard with an ancestor from their father's side. We even have similar photos of them trying to decifer the eroding inscriptions.
We were fortunate that our kids (17, 14 & 11) were all curious but relatively laid back kids with game to tackle unexpected/unplanned adventures.
It looks as if you are hoping for a similar sample of UK locations in a similar timeframe---but I hope you can do the "or more" length of vacation.
What are the ages of the travellers? Do you have any ancestral connections to any of the planned (or other) UK locations?
This forum is a great place to get, not only, feedback on plans but also questions to help you think critically about aspects you may not have considered. (As you can see with Claudia's great questions.)
Keep asking questions. There's a wealth of information from the experienced forum members. Feel free to ignore suggestions that don't seem right for you. And..it can feel overwhelming when there is so much to choose from! Come back to share your experience!
Cheryl