I don't know if it would work in the big city, but several months ago, a few of the tenants in my group of buildings started a group to plan social events, starting with one tenant who got others going. They put up flyers on the bulletin boards and convinced the building management to send out emails. We now have a Facebook group and events almost every week: a BBQ, a potluck, a movie night with DVDs, wine and cheese gathering, etc. Tonight we're getting together to watch the Perseids nearby. I've only been to one event so far, but the feeling in the flats seems to have changed. People actually speak to each other now, hold doors, etc. If someone loses something or needs a screwdriver or something, they post to the FB group.
This is in a development with flats mostly for new international employees where I work, so it's a very specific context where maybe people feel like they already have something in common. Still, I lived here maybe eight months without getting to know any of my neighbours, and all of a sudden, one motivated person has created a community.