Be prepared for insane crowds at Liberty and Fortnum and Mason. I was in Liberty a few weekends ago and very quickly left. The boutiques in Mayfair are much more my speed now.
I can tell you you will really enjoy Gymkhana, Fallow, and Brat. I have been to all of them (the first two on my last trip, and Brat back in 2022.
I am headed back the week of the 18th of December. I have a reservation at Kol for Wednesday night. Looking to book Monday and Friday night, but keeping Tuesday and Wedneday more open due to maybe needing to take folks out for work.
My list of places I want to try includes Chishuru (they reopened in Fitzrovia), Good Front Room (At the Langham), Anything in the Raffles at the OWO complex (lots of amazing looking restaurants like Paper Moon London, Cafe Laperouse, etc...), and a lot of places on this Time Out List (https://www.timeout.com/london/restaurants/best-restaurants-in-london).
Also, heard that Pacific Overtures at the Menier Chocolate Factory might be worth a watch, so thinking about that for Friday night as well.