It doesn't really seem that NCL are doing anything about the issue.
The strategy seems to be:
1. Let passengers board, and read the 'no alcohol' notices at the bars.
2. Ride out any grumbles or complaints - offer a vague explanation, passing the buck, if pressed (knowing that people on holiday probably don't have the time, inclination or internet access to pursue it).
3. Wait for everyone to calm down a bit and they start to rationalise: 'it's only for a few hours; 'it's only for a couple of ports' etc etc.
4. Disembark the passengers, who will probably grumble a bit when they get home - but so what.
5. Embark new passengers and go back to stage 1.
If a lot of the passengers aren't Southampton regulars with knowledge of other cruise lines sailing from there, so much the better for NCL.