I never saw anyone bring lunch to work when I worked in Copenhagen over a decade ago, but the at work cantinas were a lot more common than they were in Sweden.
Whereas in Sweden, the work cantinas were phased out in the 80's and the norm if you have an office job is that everyone leaves the office for lunch, and you go to a lunch restaurant, sit down, and eat your lunch. I really tried finding something similar to Swedish lunch restaurants in Copenhagen, but I could never find any. There's only "real" restaurants, which are too slow and upscale and expensive for lunch every day, or they're too fast-food-y or only really do take-away, that you're supposed to take back to the office and sit there and eat. Drove me nuts.
I have a bunch of Swedish friends who all came back from work trips to Norway, cursing, because the &¤#&#"&"# Norwegians would schedule meetings over lunch, and then everyone else would just pull up their /¤#&"&!"#&#" matpakke in the middle of the meeting, while my friends were stuck with nothing to eat, because they were used to taking a break, going out, sitting down, eating lunch, and then going back to the office. Instead, they had to sit and starve in meetings.