Check your city code website - there usually is a time they can't start construction before (and in the states, it's usually 8:00). And I second seeing if there's a legal services office available to students - they may be able to help you. I think the question you'll have to decide is - if you can get out of your lease, do you want to move. Or would you rather stay there and try to get the construction to stop (but don't want to move, even if it won't). I can't imagine there would be much time in your schedule to move elsewhere.

Good luck to you! Our city recently re-paved the street right outside our bedroom window - thankfully, it was only a few days of crazy noise, though.

CA