Never cared for it, personally. There are other European cities which have a lot of old buildings while managing to be far less cramped, busy and polluted.

Like Edinburgh. Best British city I've seen by a long shot.

However, even if Edinburgh in the Christmas time is amazing, I still am pretty sure that there are better places than either of the two capitals to go to at that time - it might be lovely in some places but overall it's not a snowy time, it's a slushy time, and slush is not something I enjoy. If you want a lovely snow-filled old town during Christmas, try a town rather than a city as the cities are just too busy to get the complete magic. Although again, Edinburgh during Christmas really is amazing, so maybe London is alright too. Just don't think classical beauty with snow on the streets, think wonderful lights and atmosphere instead.