Great Britain & Ireland - 4 Weeks and a fairly blank slate

There is no ferry to Dublin from Liverpool now. Liverpool only serves Belfast these days. That port is actually Birkenhead now - across the Mersey.

For Glasgow read Cainryan (almost Stranraer) but that only serves Belfast, then bus to central Belfast then bus or train.

The only direct ferry sails from Holyhead, Wales.

Or, if your timing was exactly right, the overnight ferry from Heysham to Douglas, Isle of Man with a morning connection to Dublin. That runs maybe a dozen times a year. Very rarely that is a Belfast to Douglas to Dublin connection.
Not the same Belfast berth as either the Liverpool or Cairnryan ferries use.

Glad you plan to do extensive traveling in the wonderful British countryside.
Oxford is good for a day and is just west of London. while Cambridge is NE of London.

Stratford Upon Avon was great, but I love Shakespeare.

Bath is worth a couple of days, good B&B is The Brooks Guesthouse and nearby Scallop Shell for great seafood.
Rent a car to see the Cotswolds, we stayed in Chipping Campden at the Volunteer Inn, which has the best pub in town and a great Indian restaurant.

Other great places in the south are Canterbury, Winchester, Salisbury, Wells, Glastonbury. Also, Windsor Castle is great.
Farther north, York is great, plan of at least two full days there.
The Lake District is good if you like the out of doors.
Durham is good for a day.

Scotland, St. Andrews and the area north of Edinburgh. Don't remember the town, but go see the tomb of Robert the Bruce.
Farther north, Loch Ness and Inverness.
Many like the western highland, but I can't say, never been there.

Ireland,
We have done much of the eastern Ireland, including Belfast, Dublin and down south to Kinsale and to see the Blarney Stone.
Haven't done the western part with Galway and scenic places like the Ring of Kerry.

We visited the Yorkshire Dales this last April and really enjoyed it. You don't say how you are getting from place to place, but a car would probably be needed for the Dales. We stayed in Hawes, but traveled down to Grassington and Malham and up to the Tan Hill Pub and all over the north area. We do enjoy walking, and the 3 walks we did were a highlight. We will definitely go back. I'm just sorry it took 5 trips before we tried it.

If you have been to Oxford, you could consider cutting Cambridge. I have been to both and actually preferred Oxford.

You have a lot of places listed. I'm sure when you sit down to decide how to lay out the trip, you may find it necessary to cut some.

TY Connie. Good thoughts.

Transport looks to me like this and that. Present thought is rental car from London to Cornwall and then to Bath (as well as points on way to Cornwall, such as Windsor, Stonehenge, Portsmouth, Glastonbury.) (6 or 7 days)

From Bath, “leisure bike” self guided to Stratford on Avon, through Cotswolds. (5 days?). From Stratford, train/bus to Lake District. (Penrith? Keswick? Windermere?) Bike in Lake District some; 2 full days or so. The bike dales? Or, train to York and bike in/around York. (3 days). Train from Lake Dist or York to Edinburgh. Train to Inverness. (6 days in Scotland) Fly home from Inverness, via London

We had a very full day in Oxford some years back with friends, one of whom lived in Hampstead and specialized in sales of rare, historic books. He had particular interest in Darwin. And so, our time in Oxford, especially at the Ashmolean and Natural Science Museums among other college sites, was well spent. Since Cambridge is out of the way from our proposed meandering path, it’s off the list, in part for the reason you suggested.

Of course, Ireland is also beyond this evolving plan.