London to Edinburgh Drive during Christmas

You do realize there is no public transport ( trains, buses or the Underground ) on Christmas Day.

Use Google to see if where you are staying is near a park you can walk to.

There will be traffic through out the route. People will travel to see family whether it be in the countryside, seaside or urban areas. If memory serves the AI is about a 7 hour drive from London to Edinburgh. 2 lanes each side and if from the states you’ll be driving on the opposite side of the road than you are used to. Also the young children need to be secured in car seats. Are you going to be lugging those with you?

From 20-24 London will be chaotic.

Christmas will be relatively quite with families out walking. Might rain, might not. Some pubs might be offering a Christmas Day meal.

England is a melting pot and not everyone will be celebrating Christmas. Some restaurants will be open but you’ll definitely need to research opening and closing hours.

According to National Rail, there is no train service between London and Edinburgh on either Christmas or Boxing day. Of all the cities you mention, the only city reasonably enroute would be York, which would be a minimum 4 1/2 hr drive. But in actuality, by the time you check out of your hotel and walk or taxi to where you have your rental car parked, then driven out of London, stopped at least once or twice for bathroom breaks and lunch at a gas stop, arrived at York, dropped your luggage, and found parking, most of the day will be gone. You won't have time for huge detours like Bath or the Cotswolds. Cross your fingers for decent weather.

You will likely need to pick up your rental car early on Christmas Eve, because most places close early that day. Everything except for some restaurants will be closed on Christmas day. But you might see if any of the airport car rentals will be open Christmas Day. Tourist places are more likely to have opening hours on Boxing day, as will some stores. Be sure to make reservations well in advance for all meals on Christmas day unless you will have your own cooking facilities. And dinner reservations for all evenings is recommended.

The driving time from York to Edinburgh is a minimum 4 hours. But, again, all the extras add an extra 25-30% to that time. An alternative would be to turn in the car in York and take the train to Edinburgh on the morning of the 27th. Frequent direct trains taking 2 1/2 to 3 hours.

Traveling on Christmas Day is not a good idea. Everything will be closed. You will get to York and everything will be closed. Most restaurants are closed and those open will require reservations. (You might find a KFC or some ethnic restaurants ope that don't require a reservation.) That's it. Not even sure if petrol stations will be open.

The UK literally shuts down for Christmas. I have spent many a Christmas in London so I speak from experience.

Having lived in the UK, please take note of what the others have said above.
If it were me, I’d stay in London, then take the train to Edinburgh on the 27th.
No driving at all.
Have you considered the weather at that time of year?
It will be dark by 4pm, and there may be ice, even snow.
No one can predict.
Especially on unfamiliar roads, driving on the left , with children.

Are you flying home from Edinburgh?

Just trying to keep you all safe .

The Lake District, or at least Keswick, is one place where things are happening on Christmas day. And it is on a direct route to Edinburgh.
So if you came up by car or train on 24 December.
There is a guided walk up Latrigg at 10am from the Moot Hall (now confirmed as happening) which ends at the Oddfellows Arms for food. Afterwards the cinema/movie theatre is open including a community screening of the King's Speech, then movies all day.
It is one of the oldest movie theatres in the UK.
People from all over the UK come up for that walk.
On Boxing Day at 10am there is another walk, this time up Catbells.
Also the lake cruises are running on Windermere (and the Lakes Aquarium at Lakeside is open). If it's a cold, sunny day like today then those winter cruises can be magic, a few years ago I was even on one when there were ice floes on the lake.
Ullswater steamers are also running.
Also on Boxing Day there is a vintage car and tractor show/road run at St Bees on the coast, supported by a free local vintage bus service, also normal bus services from as far as Carlisle, Keswick and Penrith. A!so the RNLI have a fund raising breakfast at the show.
Clearly I can't promise good weather, and don't know what accommodation is now available in Keswick, but that's what happens.
And in the Lake District generally there is a good boxing day bus service.

There may be no trains but National Express coaches are running from London to Edinburgh and York on Christmas day among many other destinations.

In London the free Christmas day routemaster vintage bus #430 runs in the Putney area,which is so popular that extra vehicles now have to be added. Also this year there is a non TfL bus #111 running from Heathrow to Hounslow (no idea what vehicles are being used). London Walks also have two Christmas Day walks (one at 11am and one at 2pm) from Trafalgar Square.

Christmas Day is not a bad day to travel. The roads are quiet and service stations are all open so there are no practical issues with making the trip on that day.

You could stop at York. I don’t think you’ll be able to do much when you arrive on Christmas Day but by Boxing Day many shops and restaurants will be open again. You’d have to check any attraction opening times.

York Minster is open free of charge on Christmas Day from 1245 to 1530 (according to Visit York) then Choral Evensong follows at 1600.

Outside tourist London plenty of people travel to visit family and friends so petrol stations are open, including one two minutes down the road from me in very provincial England, and another three minutes in the other direction.

Also Edinburgh on Christmas Day has a lot of life to it, massively aided by very good bus services. As in London you find more of that outside the very touristy parts, more where people live and work.

if you are in central London and get the car on Christmas Eve you will be liable for the Congestion Charge £15 plus your parking.

If you collect it at the airport on Christmas Day, will the facility be open, how will you get there to collect it? Taxi at Christmas rates?

From bitter personal experience I know that the roads are very busy on Dec 27th, particularly in the afternoon. People who have visited relatives for Xmas often travel home on the 27th. The 26th or 28th would probably be quieter.

How old are your kids?

Just sharing some personal experiences-

-Most things that aren't churches or service stations are closed on xmas- a bit more open on Boxing Day but still a lot closed.
-Car hire places also tend to be closed these days.
-You're correct there are no trains on xmas and very few if any on Boxing Day.
-York definitely makes the most sense if driving directly from London to Edinburgh. However if it were me I don't think I'd try to visit another location during a period when most things are closed. I would get the train up to Edinburgh on the 24th and spend the rest of the time there- you mentioned day trips and there are lots of great ones (Stirling, St Andrews, Glasgow are some of best ones, but there are loads more...). I think that would make things easier for you.
-We don't drive very often but once had to drive from the Lake District down to London on the 27th (when there were also no trains that day) and there was no real issue with traffic. I have no idea how representative that is but just one anecdote!