Bundle up. London is colder and wetter than San Diego (although I once saw it snow inside the city limits there). Winter is chilly, 30's and 40's, and windy. London is not really deluged in rain or fog, but there's certainly a whole lot more than in San Diego. Having rain on any given day is probably a 50-50 shot. Snow happens, on occasion. The most consistent thing about the weather is it's inconsistency.
It's nowhere near as sunny as southern California. It's as far north as Newfoundland. In Nov and Dec, it will be dark by 5pm or so.
Heed the proverbial advice to dress in layers in the winter. It might be 35 degrees, raining, with a 20-mph wind outside while the building you're in is toasty warm. Or, not. The Tube can be roasting or frigid.
BTW, Christmas in London can be great.