Smithfield market is a really interesting place, and if you can believe it smack dab in the middle of the market is a fantastic cocktail bar – Oriole[1]. Unfortunately they're closed now due to the coronavirus, but once they reopen I highly recommend a visit.
I am not affiliated with Oriole or Nightjar in any way, just a huge fan. (So much a fan that I've flown in to the UK on several occasions just to go to these places, can't praise them enough!)
In the meantime if you're into cocktails the bar manager of Nightjar (same owners as Oriole) has some great videos online: https://www.diffordsguide.com/g/1151/tonys-cocktails
I am not affiliated with Oriole or Nightjar in any way, just a huge fan. (So much a fan that I've flown in to the UK on several occasions just to go to these places, can't praise them enough!)
[1]: https://www.oriolebar.com/