The word Yule predates 'Christmas' in English (from gēol in old English) but it's meaning was vague. Variations of 'Yule' existed in most Germanic and Scandinavian languages (jól in old Norse meaning a feast) and seemed to describe mid-winter days and festivities. The word went out of fashion and Christmas was used from C12, although Yule carried on being used in Danish settlements and was a common dialect word in the North. (Info from The English Year book see below)
The idea that a large log of wood - The Yule Log should be burning in the fireplace on Christmas Eve or all of Christmas day was well known for more than 300 years. It had different names in various places - The block log, clog or brand but could be found all over the British Isles.
This is taken from my book 'The English Year' by Steve Roud and comes from Herefordshire in 1886
A respectable middle aged labourer tells me that in his boyhood his father was always careful to provide a Christmas Yule Log. On Christmas morning he would put a bit saved from last year's log on the fire and lay the new log on top of it, so that it might be kindled from the last years piece. Before the new log was quite burnt out he took it off, extinguished it, and put it away to kindle the next year's log.
The idea of keeping part of the wood was to ensure the luck of the house continued but it was also thought to offer protection against fire and witchcraft.
From the same book.......Folklorist Charlotte Burne recorded
In 1845 I was at the Vessons farmhouse in Shropshire. The floor was of flagstones and observing a sort of roadway through the kitchen and the flags much broken, I asked what had caused it and was told it was from the horses hoofs drawing in the Christmas Brand.
Not many houses with open fireplaces big enough for yule log now - perhaps just a few old farm or manor houses.