Christmas Markets

London has not got a major Christmas market. The markets originated from, and the best ones are in, Germany and surrounding countries.
I would suggest:

• Strasbourg. Website: https://noel.strasbourg.eu/en/
• Nurembourg. Website: https://www.christkindlesmarkt.de/en/
• Possibly Munich or Prague. Or one in a smaller town, for example Rothenburg ob der Tauber (website: https://www.rothenburg-tourismus.de/en/veranstaltungen/rothenburgs-historical-christmas-market/ )
  • Or many others

Regensburg Germany Christmas market is also a good one

https://www.bavaria.by/experiences/city-country-culture/christmas-markets/christmas-markets-regensburg/

In case you decide to keep London in the mix, here is a blog post that popped up for me yesterday. I follow this person's blog mostly because she has very nice self-guided walking routes thru various parts of the city. It's been decades since I was in London at Christmas so no input on winter market authenticity.

https://www.aladyinlondon.com/2019/11/best-christmas-markets-london.html

I have never been to the Christmas Market in London but have been to Munich, Nuremberg, and Salzburg. It is easy to base in Munich and train 1 hour to Nuremberg, and then two hours to Salzburg. We actually spent four nights in Nuremberg and easily filled the time, then back to Munich for four nights. One day in Munich we day-tripped to Salzburg as we had previously spent quite a bit of time in Salzburg. On another trip, we flew into Paris, the trained to Colmar where we based for a few days in Alsace. There is a shuttle bus out Colmar to transport visitors to the Christmas Markets in the villages of Ribeauville, Eguisheim, Kaysersburg, and Riquewihr. Afterwards, we trained to Paris where we spent three nights. Next week we are leaving to visit the markets in Vienna, Regensburg, Melk, Frankfurt, Heidelberg, Cologne, Dortmund and Frankfurt. The German/Alsacian markets have been wonderful!
We have traveled by train and there is no need for a tour. Carry a RS guidebook to visit the sights since the markets are best in the late afternoon and night. Warm coat, shoes, gloves and hat are must-haves!

Regarding RS Guide books and Christmas Market cities-
RS omits many of the smaller locations, that reportedly have great markets. We're leaving tomorrow, and I've had to complete my research , and get maps, from other sources. I've found the local Tourist Info Centers have been very responsive when I sent email requests, as I wanted hardcopy maps and guide books. Often the available online info was too small to be legible when printed.
Safe travels!

I'm not sure how you define culturally unique. But one suggestions is Jamtli, in the outskirts of Östersund (mid-Sweden): https://www.jamtli.com/en/evenemang/julmarknad/ or https://www.youtube.com/watch?v=knjkKwc4RZE Held the 2nd weekend in advent every year, and don't miss the Christmas museum as well if you go there. Or maybe Sigtuna, that is also quite popular.

Budapest, of course: http://budapestchristmas.com

I would do Stuttgart, Esslingen and Strasbourg.

Mrs. Jo, we are literally on our way, based on your advice! Thanks so much!

Here is a story about the Budapest Markets https://hungarytoday.hu/advent-feast-at-the-basilica-wins-best-christmas-market-in-europe-title/