Driving from Bath to Edinburgh - MUST sees?

I'd spend a full day through the Cotswolds, as it is so heartmeltingly lovely and the small roads get quite congested and slow.

on the a46: Warwick castle, Coventry cathedral, Lincoln cathedral

Everything in Durham - castle (part of the university now), cathedral, town. Alnwick castle, Bamburg castle.

Absolutely stunning country.

That's wonderful - thank you for the tips!

Are you planning to do all that in a day or is this "leisurely drive" going to take several days?

Google Maps tells me that it is 387 miles taking 6 hours 40 minutes driving time via the shortest and quickest route - which is certainly not the route that you have in mind. (See blue line on map).

I'm with James. That drive is going to take hours. It's far too far for one driver in a day, it could easily be 8/9 hours driving. And you are planning to stop 3 times for meals?

Thanks for the advise. Will be changing our itinerary so to begin our drive beyond the Cotswolds. But, then, we may be scrapping the whole castle sightseeing tour for an afternoon at the Nottingham races? (A very British experience?)

Agree that the Cotswolds are a must. Broadway and Stow-on-the-Wold are great places to stop. Not sure of your exact route, but York is a good idea too, if it's not too far out of the way.

It is best to take the westerly route via the M5 and M6 rather than going east. If using the westerly route, consider a detour into The Lake District for at least one overnight stop to break the journey.

Also consider going by train. Cheltenham is a good place to catch a train going north but it will be quicker to change at Birmingham - where splitting the ticket reduces the price of Advance tickets. (You could return south via the East Coast Mainline to London where you should consider a break of journey for an overnight in York).
https://www.seat61.com/london-to-edinburgh-by-train.htm

The Cotswolds, York and Durham. Stop, spend the night in each. York deserves three days.