Free market? Sure, it's a great idea, but minimum wage laws, workplace safety, pollution control and so forth have all done just as much for our health and prosperity.
It's also impossible to say whether the prosperity was due to the free market and lack of regulations, the industrial revolution and development of steam power or the rise of the middle class and their increased free time/income.
I suspect that mostly it was technology, similar to what's happening in developing nations right now, rather than any free markets.
Do you have any support for that assertion? The poor themselves decided en masse to move from village to city at the time, which seems to indicate the contrary. Yes, in the city they were also much more visible to literate observers who would write about their misery, but who knows what those same observers might have exposed if they had lived in a village instead. The people who knew both sides of the situation, certainly seemed to vote with their feet for the industrialized cities. We see the same phenomenon at work in China nowadays.
All a minimum wage law does is allow a society to shift its chosen point on an unemployment/wage tradeoff curve. However, increases in labor productivity shift that curve outward (this is usually because of technological progress and capital investment). It is because capitalism has shifted the curve outwards over time that we are so much more wealthy, not because minimum wage laws have slightly shifted our position along the curve.
If labor productivity weren't near as high as it is, then you could pass all the laws and regulations in the world and it wouldn't make us as rich as we are now. Anti-capitalists fundamentally misunderstand the process of wealth creation.
I suggest you also look up my comments on the ill-argued anti-libertarian "Victorian England" blogpost that I am assuming you are referencing from when it was submitted here.
And never mind a minimum wage law - Victorian England would've been a much more pleasant place with some sort of health and safety law, restrictions on child labour or a functioning welfare system other than slave labour in the poor house. Did you read the People of the Abyss link that I posted earlier? There's some scary stuff in there:
I worked at Sullivan's place in Widnes, better known as the British Alkali Chemical Works. I was working in a shed, and I had to cross the yard. It was ten o'clock at night, and there was no light about. While crossing the yard I felt something take hold of my leg and screw it off. I became unconscious; I didn't know what became of me for a day or two. On the following Sunday night I came to my senses, and found myself in the hospital. I asked the nurse what was to do with my legs, and she told me both legs were off.
There was a stationary crank in the yard, let into the ground; the hole was 18 inches long, 15 inches deep, and 15 inches wide. The crank revolved in the hole three revolutions a minute. There was no fence or covering over the hole. Since my accident they have stopped it altogether, and have covered the hole up with a piece of sheet iron . . . . They gave me £25. They didn't reckon that as compensation; they said it was only for charity's sake. Out of that I paid £9 for a machine by which to wheel myself about.
(from http://london.sonoma.edu/Writings/PeopleOfTheAbyss/chapter17...)
25 pounds is about 6 months wages for the loss of both legs, and he has to buy his own wheelchair! How much productivity was lost to society because that factory and others like it didn't take enough care of its workforce? And yet you and the rest of the HN libertarian echo chamber are trying to convince us that the only thing necessary for happiness is a free market?
Give me a break.
That's not the only thing it does, depending on the elasticity of various prices and wages. Another thing it does in some situations is increase the total share of money going to laborers while decreasing profit margins of their employers. This may or may not lead to the employer laying them off, depending on what the profit margins were to begin with; if they were very high, such that the post-increase margins are still nice (just not as nice), it's still rational to continue to employ the newly more expensive labor.
Consensus among economists these days on minimum wages is a lot more nuanced than it might've been 50 years ago, anyway. A majority of economists still think that they're on the whole a bad idea, but most would want to know what kind of economy you're talking about before giving specific predictions about their effects. The fundamental shift driving the "well, generally X, but it depends" view is a realization that economies can be quite far from classical equilibria, for quite long periods of time, in which case policies don't necessarily have the effects classical economics would predict.