Layers are your friend! Cuddl Duds (or similar, I usually wear the WalMart version) are great. I was in London in late December a few years ago and wore cuddl duds (to and bottom), jeans, a light weight sweater and a jacket that was a zip out fleece liner and was comfy. Take light weight gloves and earmuffs/headband/hat and you'll be set. Tights are also great as an additional layer if you don't want cuddl duds. Those inner layers are a lot lighter and will dry faster. Since those are the layers up against your skin, you don't need to wash your outer layers as often. Keeping your feet dry will go a LONG way towards keeping them warm remember so change socks during the day if your feet get wet.

Pack for 5-7 days and just keep recycling. The goal is to make it so that pieces coordinate rather than packing set outfits. 4 bottoms and 6 tops and you're set for quite awhile if all tops can be matched to all bottoms. A neutral dress can be changed entirely by accessories such as a scarf or cardigan.