We touch down around xmas eve
Assuming your touchdown is in London & you don’t want to get straight back on a plane, then Hyde Park has a Winter Wonderland with all the things you mentioned. Sadly we haven’t seen a decent fall of snow in London around Christmas for a while, so that could be the missing element.
To get the real White Christmas market feel you need to head north east to Riga, Budapest or Tallinn but these may be areas you feel are too far after an exhausting trip from Oz. This is a link to the one in Budapest: https://www.silvertraveladvisor.com/blog/destination-features-europe-hungary/christmas-market-trip-to-budapest
Nearer to home are the markets in German villages along the rivers Rhine and Danube but snow cannot be guaranteed. The most popular are probably Cologne, Düsseldorf, Bonn and Koblenz. There are many of them so I would suggest some research on the internet.
My husband, myself and our son who will be 10 at the time are wanting to visit Europe Xmas next year. We touch down around xmas eve or a few days before and are wanting our first stop to be somewhere really christmassy, I.e, fairy lights, hot chocolate, markets, father Christmas, ice skating, etc. We are coming from Australia where Xmas is very hot, so are really wanting the “white christmas” experience. I am thinking