Another fan of fleece-lined leggings here.......wearing a pair right now :)
What I would take in the way of clothing:
2 pair black fleece-lined leggings (I have LandsEnd, because they sell talls)...they have good year-end sales now. (one wear on the plane)
2 black cotton turtlenecks (one wear on the plane)
1 zip black fleece jacket (even better if it has inside pockets, too)
1 light-weight (I have Columbia) colorful fold-up rain jacket with a really good hood (that projects over glasses)
3-4 colorful scarves (not flimsy fabric, but not anything too bulky
MAYBE two colorful shawls (if going out to dinner somewhere nice)
1 hat, maybe 2 (ballcap and then one with brim for sun protection (maybe not needed in London proper in the winter, I realize)
1 pair of light-weight fleece gloves (black)
3-4 pairs of black socks
1 pair ballet flats (black)
1 pair of good walking shoes (which would be worn on the plane, too, to avoid bulk in luggage)
Enough clean underwear for a pair each day and then a spare
If you take a heavy jacket, wear it on the plane, of course, or at least wear the zip fleece jacket.
If not traveling in business or first, I have been known to pack two pillow cases, and once on board, roll up the jackets and stick them in the pillow cases to supplement the pitiful little airline pillow......I've even done that when in First.
Initial reaction might be, "but it will appear as though I am wearing the same thing each day" (except the change in scarves). Who will notice? Who will care? It is a basic from which you can change accessories.
On several previous group tours, when luggage was collected in the lobby, from time to time, I have had a tour director ask "where is the rest of your luggage." I would say, "that's it." Others within hearing range would ask how I pulled that off, adding, but "you always looked so nice." They never noticed my repeats, because change a scarf and no one notices the basics did not change :)
Have fun. Oh, and if you forget the gloves, I will never forget when we were in St. Petersburg, it was the coldest June on record, and we were freezing......again, totally without any vanity, I wore a pair of my husband's black socks for gloves. I do not think anyone "noticed," but I occasionally called attention to them with 2-3 minute "sock puppet" shows, as we discussed the freeeeeezing weather.
Travelers do what they must.
Have a safe trip!!!! And, if you need anything, you already know it is easy to shop and find things in London :)