The minimum wage guarantees unemployment to those whose productivity is not able to meet it. Like it or not, there are those in society that aren't worth £6.50/hr or whatever it is to an employer. Does the minimum wage guarantee these people a minimum income? No, it just guarantees them unemployment.
Why do you think unemployment is highest amongst the young an unskilled? Because their skills aren't yet worth £6.50. And every year the NMW gets jacked up it makes the situation worse. I ALWAYS ask - if the NMW is such a good idea, why don't they just make it £50/hr, or £500/hr? What happens then? Do you think that YOU would still have a job? Answer this question directly.
You can Thank The Lord all you like, but if it were possible to just legislate away poverty and hardship by introduction of laws that make demands of those who have more in society, then it would have been done centuries ago, but the world just doesn't work that way.