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I've been suffering from the same problem. I can log in when the game starts, but when I select Uplay from the menu, it goes to the Uplay screen and sits there for about a minute or so, then a message pops up saying, "Error. The Uplay service is not available. Please try again later." Quite frustrating, but it seems that this issue isn't just limited to 360 users, there's also issues with Uplay on PC.
Also, I'm in Australia and I just bought the game a few days ago, so you think they'd have this problem resolved by now.