10 days December Europe

https://www.christmas-markets.it/en/christmas-market-bolzano-south-tyrol.aspx

The south Tirol is different.. 50% Austrian, 50% Italian. Food, Wine, Sights. Hiking.

Any thoughts on skipping Paris due to a lot of protests and shut downs or is that over-hyped?

Never were a reason not to go there, and mostly died out. Between now and end November probably another 1 or 2 "events" which sound worse from a distance, but are in reality not a problem will both come and go.

Splitting between London and Paris is a good plan for 1½-2 weeks.
How about:
Fly into Manchester, train to York (direct train from airport), stay 2-3 nights
train to London, stay a few nights
train to Paris, another few nights, fly home from Paris.

Or, fly into Edinburgh, and do 2 nights Edinburgh, 1-2 in York, London and Paris for the rest asabove.

Since you mention London, Oxford, and Paris, I'd say give yourself 5 days in London & Oxford (stay overnight in Oxford if desired), then Day 6 would be your travel day to take the Eurostar to Paris. There are endless things to see and do in both London and Paris, as well as plenty in Oxford for a day or day and a half.

During the first week of December it will be St. Nicholas Day, which is celebrated in northern France. https://www.americancommunityinfrance.com/st-nick-a-brief-history/

If you decide to visit London in December:
See a traditional Christmas Panto
Check to see when and where Santa Runs are being held
The free Winter Wonderland ( which is especially beautiful at night) will be on in Hyde Park
Carnaby Street, Oxford, Regent Street Christmas Lights
Trafalgar Square Christmas Tree
Look for Igloos along the Thames Path especially at the Southbank Centre Winter Market
See the Nutcracker
Kew Gardens ( very popular so if you want to visit research availability)
Do you ice skate? Lots of rinks around town. Natural History Museum is a fav.
See what’s on at Flat Iron Square bear Borough Market
So much to see and do and explore

When planning your daily activities, remember that the sun starts setting at around 3:30pm. It's never stopped me, but the time for wandering sunlit streets is not the same as in June.

Christmas in London is fantastic but know that the whole city completely shuts down on Christmas Day - no public transport AT ALL and everything is closed except for a few random places. That said, we LOVED being there this past Christmas. Went to a few Christmas markets, Borough Market (which at Christmas is amazing), the service of lessons and carols in Westminster Abbey on Christmas Eve, shopping on Oxford Street, the decorations everywhere, and a beautiful Christmas Even dinner at a nice restaurant. Christmas Day went for a walk on Hampstead Heath with lots of other Londoners and cooked Christmas dinner in our little Airbnb apartment. Boxing Day we hit the sales along with the CROWDS of people - super fun! Then we headed up to Edinburgh for Hogmanay - that's a whole other experience in and of itself!

You could substitute the Alsace region of France for Paris, especially at Christmas. From Colmar to Strasbourg there are amazing Christmas markets all over the region. Many of the towns have bus links that take you from one Christmas market to the other for free or at very low cost. Since you are already considering Germany as part of your itinerary, the Alsace would be in easy reach. I had only scheduled two nights in Colmar when I was there last Christmas and stayed an extra night so I could take everything in.

Just a thought but you will have a great time regardless. On that same trip, I flew into London and went to a Christmas market in Hyde Park....it was strangely awesome. Part theme park...part Christmas market. The City looks beautiful and there are ice skating rinks set up all over London with vendors saddled along side.

Have fun!

While in London, add going to theatre. You can go to matinées as well as evening performances.