16 Nights - First trip to England

Change the order.....you are backtracking.

London
York
Liverpool/Manchester
Bath/Avery/Stonehenge/Oxford/Cotswolds
Windsor

This way you go in one direction--counter clockwise. All this can be done by train.

Liverpool over Manchester is tough. If you are Beatles fans then Liverpool. If you are football (soccer) fans then Manchester as they have the National Football Museum. If fans of neither, look into Chester instead as there is more history.

Realize at that time of the year, days are short. Sunrise around 7:45 AM and Sunset just before 4 PM.

If you base in Bath, you could look into one day tours into the Cotswolds, Stonehenge, etc. MadMax tours is popular here--I've taken them--but not sure of their winter schedule. Oxford may be easier done as a day trip from London.

Take a look at London Walks for interesting two hour tours in London and day trips to Oxford, Cambridge, etc. (Not sure of their winter schedule for out of town tours.) No need to prebook. Just show up.

I might add an extra day to Windsor - the Castle is one of my favorites. But I don't have a suggestion for which location to take a day away from.

Day 13 - 15 I assume you mean Avebury?

To visit all those destinations in 2 days (3 nights) would be extremely difficult, especially in December when days are short and a lot of what you'll want to see is outdoors. I highly recommend rethinking this. You could probably see a reasonable amount of what Bath has to offer and take a van tour out of Bath to experience a short time at Stonehenge and Avebury. Or you could stay in Oxford (skip Bath) and take a van tour to experience the Cotswolds for a day.

What time does your flight to London arrive? Many planes from North America arrive early in the morning which means you're both jetlagged and probably cannot get into your hotel for hours. If you have an early morning arrival, you might want to take the train directly to York. Save London for the end of your trip and go to Windsor as a day trip. The three nights for Bath, etc. are not going to give you enough time to see all those sites. Unless Manchester or Liverpool are of particular interest to you, I'd skip those and add time to the Bath part of the trip. As someone else suggested, Oxford may be an easier day trip from London than from Bath.

December isn’t a great time for visiting the Cotswolds as there won’t be any colour in the gardens.

Your whole schedule with the exception of York and London is far too busy. Although heading straight to York or Manchester or Liverpool may save you time, doing so whilst jet lagged and on unfamiliar services may not be a great idea. It’s not something I would want to do. You don’t have time to see Manchester and Liverpool.

It doesn’t matter if you do York or Manchester first, as neither have rail direct services to Bath and the journey time is similar.

Days 13-15 including half a day door to door between locations isn’t anywhere near enough time for 4 destinations. It’s a 5 day schedule.

The van tours of the Cotswolds I'm familiar with depart from Bath (Mad Max) and Moreton-in-Marsh (GoCotswolds and Secret Cottage). Moreton-in-Marsh is a short train ride from Oxford. So by staying 3 ights in either Bath or Oxford, one could see a good bit of the base city and take a tour of the Cotswolds. I sort of doubt there would be enough time to go to Avebury or Stonehenge, but perhaps if one arrived early in the day from ones previous stop...

Also be aware that it’s dark by 4pm at that time of year so the time available for outdoor activities such as Avebury is limited. I’d probably skip the Cotswolds as it’ll just be cold and dark. At that time of year it’s nice to sit in a cosy pub with the fire going but that in itself doesn’t warrant the trip. There are pubs like that in Bath anyway. It will be festive with Christmas lights everywhere

Not a bad plan.

I researched for our three trips to Great Britain and Ireland.

My exception for you would be Manchester and Liverpool. I can't see a good reason to visit Manchester. There are so many more interesting places to visit in the UK.
As for Liverpool, it was OK, but it doesn't make my must see list.
We also did Northern Wales (Conwy and more) as well as Southern Wales (separate trip) several castles, Cardiff, Tenby and St. DAvid's
Wales is very scenic with many, many castles.

York is wonderful and you need three nights there.
We loved the Cotswolds and spend six nights there and used it as a base to visit Oxford, Blenheim Palace and Stratford Upon Avon (must see if you love Shakespeare).
Windsor Castle is great.

And I’ll disagree as I think there’s plenty to see in both Liverpool and Manchester, I’d pick only one and maybe add a day. Liverpool is probably a bit more touristy than Manchester, there’s a really cool Christmas tree set up in Liverpool One. There’s also two cathedrals if you’re interested in the music offerings during Advent.

I’d cut the Cotswolds in December, seeing them in cold grey December won’t be much fun, kinda like planning a trip to Cape Cod in December.

Manchester has a huge Christmas market if that’s of interest to you.

Yes, of course, there are things to do in Manchester, but in my opinion, it doesn't rate high compared to so many other great places in England.
https://www.tripadvisor.com/Attractions-g187069-Activities-Manchester_Greater_Manchester_England.html

Was in London last December (2019) for my 5th Christmas stay.

A few thoughts on your itinerary.

1.) Darkness starts around 3:30-4pm in December.
2.) Majority of attractions open at 10am.
3.) As always weather is unpredictable but on each trip more blue skies than I expected. However a good waterproof jacket is a must. Only one Christmas Eve with light snow flurry and that was in the early 90’s.
4.) Read TIMEOUT London online each month before your departure dates. I’ve found interesting and enjoyable things to do via Timeout. A favorite was the Classical Spectacular that was occurring at Royal Albert Hall. One of the most enjoyable evenings I’ve spent in London.
5.) Winter Wonderland is free and a fun spot to meander about.
6.) The family might enjoy dining in an igloo that pop up near the Southbank Center.
7.) Christmas lights at Kew Gardens
8.) Carnaby Street Lights
9.) Ice Skating at the Natural History Museum
10.) Attend a theatre performance

The run up to Christmas in London is one of our favorite times in the city. Streets with Christmas lights, spectacular programs at the Royal Albert and some of the churches, groups caroling around the huge tree in Trafalgar Square, Southbank Christmas market, Winter Wonderland in Hyde park, and marvelous lighted window displays at Harrods and other department stores, to name a few attractions. You might consider the quick, inexpensive (if tickets bought months in advance), and hassle free Eurostar to Paris for around since much will be open there. England shuts down starting Christmas eve for 2 days with nothing open. We typically spent a week in each city. If you have 17 days that's just perfect for those two cities. Your proposed schedule is far too busy with traveling here and there. Check the Eurostar.com schedule to see if you might prefer Amsterdam or Brussels. For all train travel check out seat61.com where every question will be answered. Good luck choosing between cities.

In case Joy comes back...I've been collecting links for Christmas related things in London, Salisbury and Bath in anticipation of a trip in Nov/Dec.

Here are a few - some from blogs

"Best" Christmas markets in London
https://www.aladyinlondon.com/2019/11/best-christmas-markets-london.html?utm_source=newsletter&utm_medium=email&utm_campaign=lady_s_7_festive_christmas_markets_you_should_visit_in_london_a_lady_in_london&utm_term=2019-11-25

Christmas Lights in London

https://londonist.com/london/christmas-in-london/when-are-london-s-christmas-lights-switched-on

Kew Gardens Christmas

https://www.kew.org/kew-gardens/whats-on/christmas

Hyde Park Winter Wonderland

https://hydeparkwinterwonderland.com/

There are Christmas Markets in Salisbury and Bath. I suspect there are in York and other locations as well, just haven't looked there as I'm just focusing on just a couple of days out of London over 2 weeks.

There are special services in Salisbury Cathedral if you are interested. I'm going to try to go for their "Bringing in the Light" service which are the Friday and Saturday before the First Sunday of Advent (before your are planning to get there) plus the First Sunday of Advent.

You can also go to www.sunrisesunset.com to get daylight times for your various locations. Be sure to tick the box for Civil Twilight which will be helpful to you.

Thank you so much to all for your helpful suggestions and great advice. Really appreciate your responses.
Just keeping my hopes that this trip will still be able to proceed at the end of this year. We might need to postpone the trip if the covid-19 situation does not improve.
Will take this time to relook at our itinerary with your suggestions. Thanks everyone and stay safe!

We just went to the UK and spent the exact same time as you did. Here is what we did and it was wonderful and not stressful at all.
Day one - Flew to Edinburgh and stayed in hotel.
Day two through four - Drove from Edinburgh to Isle of Skye and stayed two nights in a B&B.
Day four - Drove from Isle of Skye and stopped in lovely town of Luss and stayed at Lock Lamond Arms Hotel. Wonderful!!
Day five through seven - Drove to Edinburgh and caught train to York. Stayed two nights in York. Probably my wife's favorite place. Must see town!!
Day eight through sixteen - Took train to London and wrapped up the rest of our trip.
Day seventeen - Flew home

As I mentioned...it was a stress free trip and we never felt rushed. The only thing I may have done different is to stay an extra night in Luss or York and shave off one night in London. Luss was a hidden gem. I am SOOOOO glad we took the time to see Scotland. Some people told us we wouldn't have enough time but I disagree. We had plenty of time to see all of the sites at the Isle of Skye and the scenic drive from Edinburgh was wonderful. We took A9 on the way up and took A82 (Glencoe) on the way back.