Not a fan of any of the pubs down there. Depends on context but we aren’t allowed to frequent such watering holes as someone got in trouble down there. Gives the wrong impression.
Honest Burgers is nice near Bank though. Worth the walk.
Back when I started work in the City, the drinking culture was rather different than it is today. Particularly when the US banks moved in in the mid 90s and took over, the lunchtime drinking thing pretty much disappeared, although it still pervades to some degree in the insurance markets around Leadenhall Market. Insurance, by the very nature of the need to spread risk, fundamentally remains a personal networking thing.
The City pubs used to close at 8:30pm when I started working there, I guess that gave enough time to sober up for the next morning, although typically for those of us working in the boiler room with a thirst on and not let out until 6pm, we headed into the West End after that. I can't do that now on a regular basis as I did in my 20s, I'm far too old and far too aware of my own mortality!
In the investment banks, it turned into a permanent case of watching your own back, everyone afraid to leave their desks for fear of missing a call from across the pond and you weren't there.