Hello from the UK!
I had two quick days in London before heading north, and as I only had one real day of daylight, I mapped out a little tour of bookshops. As always, this is by no means comprehensive nor a claim to be "the best" of anything. They're literally shops I saw photos for on the interwebz and thought they'd be cute IRL (spoiler: they are!)
I started the day later because I woke up having no plan then mapped this out after consulting friends' resources (thanks, Carlie! thanks Alana! thanks Jane!) The pace is slow and wandery with lots of stops for snacks:
Start with a coffee and second breakfast at Knockbox Coffee (I'm assuming you'll have slept in and eaten first breakfast already). On the same road you'll find Persephone Books, which publishes "twentieth century women writers." The shop is tiny, cute, and doubles as the publishers' offices. I was excited to see a shop centered around women (lots of women writers, suffrage posters, etc), but upon asking if they had any recommended reading by women of color, the staff person replied, "no, not really. We've tried but there just aren't really that many so everyone else always snatches them up." Alrighty then, white feminism.
(At this point I stopped at Fabrique to pick up a cardamom bun for later).
From here you can head to Quinto. You might want to pop over to Dishoom first and see if they have a line. If they don't, get your ass in there. If they do, browse through Quinto while you wait. This shop has two floors of secondhand books. If you love the old book smell, this place will be your jam. Regardless of whether you go to Dishoom before or after, make sure you know their chai is bottomless (a sad realization I only came to much later in my meal).
By this point you'll need to digest, so the long walk to Daunt could be nice, but I won't judge you if you take the tube. Daunt is beautiful and mostly travel books (though a nice selection of other things like fiction, cookbooks, etc). From here you can walk and dawdle along Marylebone or if you're me, haul ass to Heywood Hill to catch it before the sky turns too dark (this is what happens when you go to London in January). Heywood Hill is another tiny, cute, mixed-office space bookshop which offers home library design services. I didn't know this was a thing and now I'm ready to change careers.
At this point, I'd planned to go to John Sandoe but ran out of time/steam, so I took the tube home, ate my cardamom bun, and called it. Seeing how there are so many bookshops in London, I'm excited to repeat* with new shops during my next visit. Any and all recommendations welcome!
*preferably sans white feminism