Totally agree with you matts1. If they put the prices up the scumbags/chavs that usually cause drink related problems will just resort to thieving to get the money to fund their drinking as they already do to fund drug habits. As you suggested it should be made harder for them to get the alcohol, that way even if they have the money they can't get the booze (or at least not so easily).
The next step is to make punishments more severe for anti social crimes. At the moment there is no incentive for chavs to behave as they know they won't get punished when they are caught misbehaving.