Wednesday night in London - what to do near the Gerkin building?

Sky bar in the walkie talkie building if you can get in. Usually a reservation needed, but middle of Jan and poor weather, you might be lucky. Views might not be up to much though.

Or a proper London boozer.

Have a burger. Hth.

There's a swingers place just up the road. You can probably hook up with a couple and make a three or foursome if so inclined.

https://www.swingers.club/uk/venues/city?utm_source=google&utm_medium=organic&utm_campaign=gmb&utm_content=city

(It is SFW)

Lots of old boozers around Whitechapel - Jack or Reggie if it takes your fancy. Blind Beggar is supposedly the most famous pub in GB

George Tavern for music £5.50 ticket tonight for up and coming (or maybe they'll never make it) bands. All live music is great. https://thegeorgetavern.london/

Might be a bit late if it's for tonight, but jump on the tube and go see a show?

https://www.londontheatre.co.uk/whats-on

Bill Bailey is on at the moment for example... https://www.londontheatre.co.uk/show/39210-bill-bailey-thoughtifier

A quick tube ride from Aldgate over to Barbican and a short walk will get you to The Slaughtered Lamb, tucked away around the back of Smithfield Market. Not a bad pub, and they have live music, so might be worth checking out.

Does it have to be a bar?

Last time I was in London I had the option of going to the pub with my work colleagues, who I had just spent all day with and would spend all day tomorrow with, or making my own entertainment. I ended up at the Vauxwall, an indoor bouldering place under some railway arches in Vauxhall. Had a great night, probably the only place in London I would feel comfortable walking in not knowing anybody and just be able to make friends with random people, they were all lovely. Definitely recommended. And it has little cafe bit if I remember right