The Christmas tree was a Germanic custom, and was popularised in Britain by the Hanoverian royal family during the late 18th and early 19th centuries.

Prince Albert, the husband of Queen Victoria, is often wrongly credited with introducing the Christmas tree to Britain. It's certainly correct that Victoria and Albert helped to popularise the tree among middle-class British families, as their tree-decorating tradition was covered in the popular press and set a fashion - for example, see this 1848 engraving in the Illustrated London News; as well as this 1857 photograph of the royal tree at Windsor Castle, for an idea of how a 19th century tree looked.

However, the first recorded Christmas tree in Britain was introduced by Charlotte of Mecklenburg-Strelitz, the wife and queen consort of George III. Charlotte came to Britain as a young German princess in 1761, but it was not until 1800 that she is said to have established the royal custom of erecting a Christmas tree, which then spread among the aristocracy. See this article for more information. Before the advent (no pun intended) of the Christmas tree, however, there was a longstanding English tradition of Christmas greenery stretching back to the Tudor period, in which branches and wreaths of holly, ivy, myrtle and willow were hung in the home, and permeated with fruit and spices. This blogpost from English Heritage has more information on the types of greenery used.

Interestingly, the idea of Christmas greenery and the Christmas tree seems to have been associated with Protestantism. This isn't a historical area with which I'm fully familiar, so am hoping someone else can comment, but I believe the custom of erecting a tree was found more in the northern Protestant/Lutheran German states, than in the heavily Catholic southern ones.