I went to London at the back end of Nov and I wore a sweater dress, patterned tights and knee length boots for the day and in the evening, I wore a simple shift dress, high heels and a wrap. To come home in, I wore leggings, the same boots and a sweater dress (different to the one above),
I live in central London, and cabbageroses is right, people wear everything! Personally I find a good coat is a godsend, if your out and about it doesn't matter what you wear underneath.
How about: Skinny jeans tucked into boots, with a breton top and a smart, cashmere or well fitting jumper with a good coat over the top. Or A good pair of boots, thick woolly tights, a mini skirt and jumper.
If you buy anything I thoroughly recommend Brora jumpers. Otherwise a good pair of jeans, a fab timeless coat and an amazing pair of black heels are all staples that you can justify (at least to yourself ) spending money on.
Actually, you do see boots of absolutely every kind here in London, so I wouldn't necessarily be put off them if they're comfortable.
Btw, the first outfit bambi describes (skinny jeans, etc) is more or less my default London 'uniform', though have been known to wear skirts and dresses too on occasion. Anything you feel good in goes realy, as long as not OTT or too hot.