Hi, I would also look into places you can reach by train from London. Some ideas would be Bruges, Antwerp or even Maastricht (NL). They all have excellent Christmas markets and a cosiness to complete the setting.

how about Hamburg?
 

I'd go for Copenhagen, due to shorter flight time and good availability of cheap flights. Its airport has good connectivity with city centre.

Hamburg can fulfill your criteria, too. It has a Scandinavian flavour.

Both are quite windy.

I just wanted to update this (five years later) and mention that I would up going to Vienna, and absolutely loved it! Saw all the Christmas markets, drank a bunch of Gluhwein, and wandered a ton.

Better late than never!