My subjective opinion, coming here from east coast US and living in London: it rains a lot less than the stereotype (I don't think much at all!). The winters rarely get really cold (I get by with sweaters and a trench coat). What really does me in is the lack of sun. I don't know what the official stats say, but to me it feels like you rarely see the sun from about now until early March.
But, I do think there are lots of things to do to deal with it! I hear the SAD lights are really helpful but even things like getting a nice teapot and candles for the home, taking hot baths, finding a local pub that's really toasty, things like that.
I also highly recommend, if you can, taking advantage of the budget airlines and taking a mid-winter break somewhere sunny in the Med or somewhere (you can get cheap flights to loads of places, even north Africa...) Last January I did a really cheap weekend away in Madeira, 2hour flight, gorgeous weather and food, and it really killed my winter blues.