Because it is outlawing a practice that has no victims and from which everyone benefits.
I must confess I'm not sure whether the minimum wage legislation as a basic principle is a good thing or a bad thing. I can see the arguments against, that it distorts the market, and the arguments for, that it protects exploitation of those at the lower end of the income scale. I'll let those who understand more about economics than I do decide whether the minimum wage legislation as a whole should stay or go.
However, if we are going to keep this law, then we need to make an exception for internships. Currently, it is illegal for employers to offer unpaid internships. This is a great shame. Internships can be a great stepping-stone for recent graduates, who can find it very hard to find work if they have no experience. They often lead to permanent jobs in the same organisation, and even if they don't, then the experience that the interns can put on their CVs can be a great help in finding jobs elsewhere. And of course the employer benefits from having an extra pair of hands at no cost. It's a classic win-win situation.
Maybe in an ideal world all internships would be paid at the minimum wage, but in real life many employers simply can't afford to pay, and so internships that would otherwise be available just don't exist.
Oh, and by the way, how come MPs can still advertise for unpaid interns for their offices? Is this another law from which MPs have a special exemption?