What to wear in a UK winter

I always wear an under shirt or cami tank under my long sleeved wool tops and then a coat when ever I go out on freezing days. I can't stand the wind so I also wear some sort of hat and scarf if it's super cold out to keep my head warm.  

I second this suggestion. Even just wearing a cami under a t-shirt was enough warmth for me on many days.  Primark has some for £2 that have a shelf bra built in, but I always wore a bra under it as well.  I also picked up a 2-pack that didn't have a shelf bra at Debenham's for £8. The important thing is to make sure the cami is long enough. If you can tuck it into your trousers, then you don't have to worry about a chill on your lower back if your pants slide down.

If I was just at Tim's house during the day, I'd wear sweatpants or fleece lounge pants to stay warm and only wore jeans and cords when I left the house.  

Also - it's surprising how warm a pair of tights can be, either worn with a skirt or even worn under jeans.

When we were out and about I always made sure I had a bag with me (tote or a backpack) to discard my layers into if I took things off.

As far as hats go - Tim bought me a fleece lined woolen hat in Hay-on-Wye that had ear flaps.  If it was particularly windy, I'd tie it in place under my chin. Looked silly, but I stayed warm!  I also discovered just how much I love flip-top mittens last winter.

ETA - and underwear matters.  plain cotton panties will keep you warmer than silk or synthetic.  I really liked the boy short style as it guaranteed butt coverage! 

Brilliant responses - thank you all so much! It's sounding like a good jacket is the key item to have. I'm in a hot part of Australia at the moment, which has a winter that is probably warmer (and certainly drier) than a UK summer. So I'm imagining that my 'winter' coat is probably not going to be much use at all over there and I will need to invest in a good - waterproof - one as soon as I arrive.  We have some scarves and hats that will hopefully serve us well. My daughter visited a snowy part of NZ last year and has a fleecy hat with ear flaps that I imagine I am going to covet! I have a very large woolly scarf that I've never been able to wear over here, but hopefully that will suffice for the UK winter. While my daughter has some sweatshirts, I don't really have any warm tops. I'm getting the sense that a t-shirt/long sleeved top, thin cardigan, jacket is not going to be enough layering?

I'm moving to the Midlands. The house I've rented is only a couple of years old, so I'm hoping it will be quite warm. I plan on doing lots of walking outside even in winter (am I being overly optimistic?!). I'm wondering about the wetness though - do people use that waterproofing spray? I'm thinking that might be useful on shoes and jackets ... but don't know if it works all that well.

Thanks again.

Where in the Midlands? I'll be in Lincoln...last Winter, I did a ton of walking, both in town and on the local footpaths. The worst for me was early Spring (March/April) when the footpaths were muddy and icky.  If you do plan on mucking around when it's rainy/muddy, get yourself a pair of Wellies!  If the price tag on the actual Wellington Boots scare you off, you can easily find waterproof knock offs most places that sell shoes/boots. I got mine at B&Q in the gardening section.