When governments rather than markets set prices, it fucks up the economy. Wages should be determined by market forces. Whether they enable you to live in a palace, or sleep under a hedge, is irrelevant.
To be clear, I'm not advocating that people be left to sleep under hedges, I'm fine with the benefits system preventing that. But it is definitely not the job of employers.
It would be extremely damaging to the economy to fix labour costs at a level substantially different from where they would be if there were no minimum wage. The net result would be millions out of work, and many businesses (and public sector functions) no longer viable.
Theoretically, to prevent the damage caused by artificial labour prices, the ideal option is that there should be no minimum wage. In practice, since it was introduced, it has been set at reasonable levels which appear not to have caused too much harm, and I accept it may have done some good.
If we are going to have a minimum wage, the criterion for setting it is that it must be set at or below the level where it starts to destroy jobs. As far as I can tell, it has always been set at about that level.