They have risen, but a recent study showed that they rose ever so slightly more in northern England. As such, they are concluding that MUP has saved lives.
But this also negates the very real point that MUP is utterly devastating to hardcore alcoholics. They stop spending money on things like food and heating to keep drinking, making their health outcomes worse. In effect, the very people this policy is designed to "save" are being harmed by it.
As @Todd_is_God says, the answer always seems to be that it isn't expensive enough. Heard a guy on Radio Scotland yesterday saying it needed "reset" to 70p a unit. A 40% jump in costs.