OP that is a very ambitious plan! London is heaving atm so as others have suggested you need to limit yourself to one area, take it slowly, enjoy what it has to offer and not worry about trying to battle through crowds and traffic. I would suggest one of these three plans.
Covent Garden, lots of small, rather crowded shops, but a good variety, also a market area with various things on different days, all looks beautiful, lots of places to sit down have a coffee and people watch. One of our favourites is the roof top bar at the Royal Opera House. Downside is quite uneven walking surfaces, lots of changes of material underfoot and unexpected changes of level.
Fortnums, such an amazing shop, gorgeous displays, their windows at Christmas are legendary. Fabulous perfumery department and Christmas shop. Within the same area you also have the huge Waterstones, Santa Maria Novella Pharmacy ( yum), Burlington Arcade, Royal Academy for your soul. Again lots of places to sit and eat have coffee, including quite a few chain places so not too exorbitant. Downside is you will need deep pockets and willpower of iron.
Marylebone High Street, not quite as glamorously “London”, but great range and variety of independent shops, cafes , etc, also a few (pricey) charity shops which you wanted. All make a great effort to put on a show. Nearby is the Wallace collection if you need a respite from the mayhem. Downside is quite narrow pavements and an inordinate number of tiny dogs!
I think your biggest issue is going to be getting around, even with a blue badge you are going to struggle with finding parking, and unless you are used to London traffic I think you will end up traumatised by driving through pre Christmas London streets. I am used to London driving and I would not drive into central London in the daytime for a thousand pounds at this time of year.
Public transport is your salvation, park up somewhere on the outskirts near a tube station and plan your journey from there. TFL website will help with this, it lists step free tubes and you can plan journeys that are minimal walking.
I hope you have a lovely day whatever you end up doing. I love people coming to my city, think it’s the best place in the world ( slight bias showing). Keep your belongings safe because there are mean people about, as there are everywhere, a well zipped shut cross body bag is best.