Route from Paddington to York

They're both a bit of a slog to get to from central London and there's not really much in it. As to the journey, despite being a motorway, the M1 is usually the slower way to go--speed restrictions and heavy traffic really slow you down. The A1, despite only being motorway in parts, is often quicker and less stressful. You'll see more countryside from the A1 (though in truth, still not much worth seeing) and it's easier to get off to somewhere nice quickly.

Take your own sandwiches--they're ferociously expensive in the service areas.

"Looks like the most confusing and time-consuming part of the trip will be getting out of London" - you are right there, recon 1 hour plus (depending on time and day) to get out of London (to the M25).
I would vote A1. The M1 is a motorway, 3 lanes in each direction, you will see countryside, but you will be flashing by it. The A1 is a dual carriageway, mostly 2 lanes in each direction with some roundabouts. It is the original road from London to Edinburgh upgraded many times. It now bypasses all towns and villages, but it still has some local roads turning off it at "normal" 90° road junctions, and you may even get a tractor or a bicycle on it. It will be slower than the M1, but give you opportunities to turn off into the towns that are bypassed. For example Grantham, Newark.

But, I would not do this by car. Getting out of London will be a nightmare. I would strongly recommend taking the train to York. Two trains per hour at 125 mph, trip takes 2 hours, http://www.viamichelin.com/ says 4h07 by car - twice the time. And that is assuming no "comfort" or other stops. Also, you do not need a car in York. If you need a car for after York, you can pick it up in York.

I wouldn't drive either option from central London if hiring a car, as I would get the train to York and hire from there. I drive the majority of this route when visiting my parents and these days, I tend to use the A1, but the scenery isn't exciting.

The disadvantage of the A1 is that it's mostly just 2 carriages (M1 is 3) and if there is a crash, as there was my visit before last, then the whole road gets blocked. This added over an hour to my journey. Over the past decade, most of the roundabouts that plagued the A1 have been replaced with junctions, so the traffic isn't stop/start like it used to be.

Well, if we had it to do over again, perhaps we would not get the car.....but we are using an American Airlines Vacations package, and we must pick up the car the day we arrive. Our trip for three people, all adults, is already purchased and non-refundable. So we are planning to park at our B&B while we do London by public transport, but then drive a circle tour. We did fine doing this in Ireland a few years ago, so not concerned about the differences in driving, etc. We live in a rural area of the US, and are used to driving everywhere - never occurred to us not to get a car before we started reading the forums.

Sue, can you park at your B&B in London. Have you asked them?
Sussex Gardens, like most of central London, has yellow lines along both sides (= no parking). What parking there is is liable to be residents permits only or meters, i.e. you can't park all day. Try looking at your B&B on Google Streetview. At least you are not within the Congestion Zone charge area.
You may also have problems parking all day in York.
What places are you planning to stay in apart from York or London?

If you do decide to take the A1, I would recommend Stamford or Grantham as places to stop for an hour or two.

If all you are doing is London and York then a car is more trouble than it's worth. Can you just forget to collect the car - what's the downside of that?

Thank you for your replies.
We are staying at the Mitre House Hotel http://www.mitrehousehotel.com/mitre-house
We specifically chose it because it had free onsite parking. And triple rooms - not easy to find!
We are planning to drive all around Great Britain, not just to York. We will be going some places where a car will be very useful, I think, such as Snowdonia in Wales and the Cotswolds.

My suggested route:

A40 (Westway)
M40 to Junction 10
A43 to M1 Junction 15A
M1 to Junction 21A
A46 to Newark
A1
A64 to York

This may be more lengthy but it has the following advantages:

• easy and simple route out of London
• avoids the worst of the current M1 construction and most of the substandard parts of the A1 (there are some areas with construction but are generally free-flowing)
• a more of a cross-country route especially the A46, but still all dual carriageway or motorway standard, apart from a short stretch around Newark.

You must be happy with roundabouts though, especially on the A43.

Sue, when you look at the google street view and see all those parked vans, if you swing the little man around you will see all those road works.

That is for CrossRail, the new under ground train line being built. Although the photo was taken in 2014, I would be very surprised if all that is gone. CrossRail, now called the Elizabeth Line, is an absolutely vast programme of building making a real mess of London where it is being built.

You might like to ask your hotel if it is all still there, and if there is a lot of noise.

I wouldn't advise cycling in the vicinity of a CrossRail site. Too dangerous.

Are you planning on leaving London via the A40/M40?

I know that you are committed to the car now, but I will pile on with the others for the London/York segment. I'm sure that you will enjoy it but it won't be particularly scenic.

If you see reduced speeds advertised for an area of road works, heed that speed. Those yellow columns along the road with a blue M on the top (other models are also available) are speed cameras which not only record your speed as you pass them but also your average for the full duration of the works. Expensive tickets result from speeding in those dangerous areas. A common trick is to see the cones disappear and a national speed limit sign off in the distance and everybody speeds up, and just before that final sign there is one last speed camera. All that grinding slow driving bumper to bumper for all those miles all undone in moment of lead foot.

"Many phenomena‑wars, plagues, sudden audits‑have been ad­vanced as evidence for the hidden hand of Satan in the affairs of Man, but whenever students of demonology get together the M25 London orbital motorway is generally agreed to be among the top contenders for Exhibit A. Where they go wrong, of course, is in assuming that the wretched road is evil simply because of the incredible carnage and frustration it engenders every day.

In fact, very few people on the face of the planet know that the very shape of the M25 forms the sigh odegra in the language of the Black Priesthood of Ancient Mu, and means "Hail the Great Beast, Devourer of Worlds." The thousands of motorists who daily fume their way around its serpentine lengths have the same effect as water on a prayer wheel, grind­ing out an endless fog of low‑grade evil to pollute the metaphysical atmo­sphere for scores of miles around."

Terry Pratchett and Neil Gaiman, "Good Omens"