The only way that minimum wage laws don't cause unemployment is if they are set lower than the market rate. As soon as they go above the market rate, they cause unemployment. Whether this is fair in neither here nor there. Fairness doesn't come into economic laws any more than it impacts the laws of physics.
Don't believe me? Okay, why don't we set them to £10 per hour? Or better yet £20 per hour? Do you not think that will cause immediate unemployment to a vast number of people currently working below that level? You may concede this point, and come back and say, 'yes, but no one's saying we should set it that high'. No, because even the most dunderheaded interventionism shills accept the truth. So, if you accept £20/hour is too high, how will we know what level they should be set at? What is the economic calculation that should be employed by the central economic planners? I'll wait a little while, as you rifle through your graphs and mathematical models ... give me a shout when you've got an answer, I'll be banging my head against that brick wall over there.
UPDATE: A commenter, Lee, pointed me to this clip from Peter Schiff, which gives a good example of the issue in question: