I don’t think people realise how rare it is. There are only 8 recorded white christmases in London since 1900.
So why the association is a fair question. There is a very simple answer to this. Charles Dickens.
During Charles Dickens’ childhood there was an unusually high number of white Christmas. 6 out of 9 of his childhood christmases were white. One winter it was so cold that the Thames froze over so thickly they were able to hold market on it. Someone even took an elephant out on to the ice. All this later reflected in his writing. Particularly A Christmas Carol.
Dicken’s writing was not enough to embed it so strongly in the British mindset though. What happened next was the advent of Christmas cards. And where did the Christmas card industry look for inspiration for their pictures? That’s right. Dickens. A significant number of early Christmas cards (and still today) show Dickensian street scenes.
All this is then repeatedly reinforced today by the advertising industry and media.
Hence the image of a perfect British Christmas being snow covered ground, carollers in top hats and robins in the trees. It’s all down to Charles Dickens.