I've been to London in November a few times. Most recently, last November, 5 - 13. As Erica experienced on her slightly overlapping visit, the weather was cool and there was some rain.
As to clothing, I could wear layers in case it got really chilly. My mainstay was a raincoat (not heavyweight, i.e., with no winter liner) that I'd bought at Costco. It's very water-repellant, with a good hood and nice pockets, just above knee length. It was just right as an outer layer regardless of rain, and was brilliant in the rain.
I'm in the habit of treating my shoulder bags and shoes with water repeller spray, and made sure those items I took on the trip had been freshly treated. That served me well in the rain. Obviously not totally waterproof but nothing got drenched or ruined or even very damp at all. I didn't bother with an umbrella, just raised the hood on my raincoat as I walked around London when it rained.
BTW I didn't experience solid days of rain. There were a few days where serious rain showers moved in by late afternoon and persisted into the evenings. Otherwise it was fine. I don't recall that I was kept from going anywhere I'd wanted to, because of the rain. (Although TBH there were evenings when because of a combination of fatigue and rain, I picked up some takeaway for a light supper in my room, vs. going out again.)
As mentioned, temps were in the 40 - 50 (F) range, IIRC. I was comfortable in the raincoat. I'd also brought a very packable puffer jacket, but I don't think I ever felt cold enough to wear it on that trip.
And yes, they were getting the Christmas lights up although it was still a little early for the full installations. My reason for visiting at that time was to be there for the centenary of the WWI Armistice, and I'm so glad I was.
My problem these days with walking in London, is rarely weather, but rather the effects of age on my stamina. I hope you have a great time there!
BTW, the only bitter cold weather I've experienced in London, was in February a long time ago. (It was a theatre break, timed to take advantage of the US President's Day holiday weekend.)