I live in Sweden. Those are my qualifications to answer. Middle of the country, not the worst weather but not the mildest either.
You need to think layers and not rely on one warm item. You also need to think of what fabrics you're wearing.
Layers keep you warmer because between each layer air is trapped that heats up and keeps you warm. Certain fabrics work the same way by being by their nature "fluffier" so traps air within itself and keeps you warmer. The thicker they are the more air they can trap (I simplify, but you get the jist). This is why a brushed cotton or flannel shirt will feel warmer than a denim one, even if they are the same thickness.
Look at wool, and if you can't stand wool (allergy or whatever) then look at synthetic fabrics specially made for the cold, like micro-fleece or Uniqlo's heattech range or similar.
Make sure your shoes are not too tight, because you need wiggle room to trap air. If you wear two pairs of socks the whole thing mustn't be too tight, you won't get any air trapped and you won't be able to move your toes to keep circulation going.
Shoes have to have a winter appropriate sole. It has too be thick enough to insulate from the cold in the ground.
So - something thin and fitted near the body (vest or sleeves depending on cold/situation). "Normal" clothes on top. If your normal clothes are winter appropriate, for example made of wool and not polyester, you get another layer of warmth there. Just keep building layers depending on how cold it is. There is a reason why people used to have a summer wardrobe and a winter wardrobe - the materials used were different. Now everyone wears the same Next polyester trousers all year round and is surprised at melting in the summer and freezing in the winter.
I wear wool socks from October - I buy good ones made from about 80 % merino wool. I have thin ones and a thick kind, and I combine them depending on temperature.
Be very wary of things that have the shape of winter clothes, but not the materials/functions. Like fashion boots made of fake leather (traps sweat which chills your foot) with a cutesy fake fur trim at the top. Looks like winter, is not winter. Or "wool" coats made from either synthetic fabrics of poor quality and/or just too loosely woven to keep the wind and cold out. You need things that trap the hot air next to your skin, not stuff that lets it waft out directly.
I don't know how available these are in the UK, but like all middle-aged women in Sweden I own a padded skirt. www.outnorth.se/klader/kjolar-klanningar/tackkjolar
I find this so handy for just popping on over whatever I'm wearing, it traps a bit of heat and is easy to take off when I arrive. I find dressing my legs warmly in the city is the hardest, because if you wear a base layer and then trousers you die of the heat when you get indoors. The padded skirt means I can wear just ordinary tights and a skirt/dress or ordinary trousers, and still be fine.
My 20-something daughters wouldn't be seen dead in it of course. But they'll get there. They will.