Gordons wine bar, I used to work next to it and would visit almost every evening to grab a bottle for my wife and I as well as some decent cheese.
It's Londons oldest wine cellar and it's based in Embankment. Certainly something only the 'locals' visit with tourists rarely there. However, I last visited maybe 7 years ago?
https://www.gordonswinebar.com/
**** me, I totally forgot about this place. Used to go there as an undergrad. Haven't been in 20 years.