Great Britain trip

Can you give us a clue as to what you are interested in seeing and doing? Twenty mile hikes? Contemporary dance? Norman castles? Puffins?

What drew you to England other than London? You really need to do some research on places and things of interest to you, then come back with focused questions. Nobody can adequately answer a very generic question without additional information, e.g., whether you like museums, cathedrals, Neolithic sites, castles, villages, towns, cities, sporting events, WWII sites, nature, etc. A person could spend a month in each Wales or Scotland, or any part of the country and not see everything there is to see. If you want someone to plan your trip for you, you may want to find a travel agent.

As others have said we need to know your interests. If you are doing mainly cities then a car will be more of a hindrance than a help. So your first 5 days in London certainly no car.
If you want to spend 4 weeks in the wilds of Scotland a car is essential, pretty much.
Great Britain is almost 1,000 miles north to south, 400 miles or so wide at it's widest point, plus islands so it is essential to narrow things down.
We could put you on a 4 week history itinerary, a 4 week art trail or a month walking the South West Coastal path, but if none of those things interest you they won't work.

In short , get a Rick Steves guidebook , do some studying , and then come back with specific queries , Happy planning !

I suggest you buy this guidebook:
https://store.ricksteves.com/shop/p/britain-guidebook

There are pages at the beginning to help you plan an itinerary, and also some suggested itineraries.

There will be a new version in March if your trip isn't soon.

We love Great Britain and have traveled there several times. Our last trip was a four week drive tour around S. Wales and England with no time in London.

We visited
Bath
Wells and Glastonbury
Tintern Abbey and other castles on our way to Cardiff
The Museum of Welsh Life and Pembroke Castle
Tenby, Wales
St. Davids Wales and a couple more castles
The Cotswolds (stayed at Chipping Campden at the Volunteer Inn) using it as a base to do the Cotswolds, Oxford, Stratford Upon Avon and Blenheim Palace
Warwick and its castle
York (must see)
The Yorkshire Moors and Whitby
Durham
Hadrian's Wall near Haltwhistle
The Lake District, stayed at Keswick
Winchester

Also, we have spend time in N. Wales at Conwy and some very scenic places, Cambridge, Windsor Castle, Stonehenge, Salisbury and Southampton.
For Scotland, Edinburgh is tops, with St. Andrews and the area north of Edinburgh. Also, Lock Ness and Inverness.

That's a lot of territory and so a broad range of possibilities. London for sure is worth 5-7 days. Other than that, without knowing where your interests lie, here are links to a couple of Trip Reports I wrote after trips to Scotland and England last year. Maybe you'll find some nuggets in these that will help with your planning.

https://community.ricksteves.com/travel-forum/scotland/in-search-of-jamie-fraser

https://community.ricksteves.com/travel-forum/trip-reports/trip-report-the-south-of-england