You can get beer almost any hour of the day as long as you do your research in advance. Long before the new 24-hour licensing laws it was possible to drink for 24 hours in Edinburgh (you did have to spend a couple of hours sometime around 4am in a resteraunt).
About 7 years ago I used to work in a pub that opened every morning apart from Sunday ay 7am. We used to have happy "hour" 7-11 every morning