I'm not sure about England, but in Ireland and possibly other Celtic countries, Winter is traditionally taken to be November, December and January, thus Christmas is just slightly past mid-winter.
But apparently that's indeed the long-standing date for the festival to mark the start of spring [2]. Guess those are some chilly festivities!
In those days the amount of light available was a huge issue and feast days were marked around the days the light shifted, as well as shifts in behaviour. For example the harvest work would traditionally begin the day afer Samhain, halfway between the summer solstice (Midsummer) and the autumn equinox.