Matt I am often in London in November. In fact one of my favorite months to be there. Yes, take a water proof jacket and layer but know in the past decade over numerous visits very little rain. Some but not daily nor torrential.
Neighborhoods: Kensington, Chelsea, Fitzrovia, Pimlico and Earl’s Court. Sites are spread out but with Oyster cards you’ll be able to see all that you wish.
London will be decked out for Christmas. The fun, colorful (neon lights) and free WinterWonderLand will Be On in Hyde Park. Check the web for turn on dates for Carnaby Street, Regent and Oxford Street Lights, and those at Kew Gardens.
Also Time Out Magazine for Santa Runs, Pantos and other interesting events in November.
Use Google Satellite View and type in Big Ben. Zoom out a little and you’ll see what’s close to Parliament Square. Easy to walk from there across Westminster Bridge to the Eye OR up Whitehall to the Horse Guards and past 10 Downing Street to Trafalgar Square and over to Covent Garden OR up Birdcage Walk through St James Park to the Palace. Looking at London via the satellite view you will also be able to see all the Underground stations. Look for the iconic Red circle with horizontal dark blue line thru it.
If there is an interest in Henry VIII an easy train trip to Hampton Court Castle is a must. It will all decked out for Christmas.
Great choice Matt. Have a great visit.