Okay, I am not going to pretend like I am educated on exactly what happened, but from what it seems like there was lots of government interference leading up to and during the famine. Like most arguments against supposedly free markets, it takes a crisis from within a state-controlled economy and argues it as an example of why the free market is dangerous. The first article brings up the article from Mises that argues the opposite view but doesn't really refute it, saying:
"Modern day advocates of laissez faire argue that the famine was caused by too much government interference. Like the argument that the Financial crash of 2008 and the resulting depression was caused by too much government interference, this is a position based on pre-conceived opinion rather than any evidence. Therefore there is little need or point in refuting it."
He frames his arguments under the pretext of limited, half-assed schemes that didn't do enough, but the system in English-controlled Ireland doesn't seem at all laissez faire. The Mises article he metioned notes British Corn Laws, English protectionist policies, and The Bank Act of 1844 as being a major factor in causing or exacerbating the famine. Here's an except from the Mises article:
The British Corn Laws were designed to protect local grain farmers from foreign competition. In 1801, these laws were extended to Ireland. The laws not only kept prices high; they protected against falling prices in years of plenty. The main beneficiaries of this protectionism were the English absentee landlords of Ireland, not the Irish.
The Irish people were able to grow large quantities of nutritious potatoes that they fed their families and animals. Landlords benefited from the fact that the potato did not deplete the soil and allowed a larger percentage of the estate to be devoted to grain crops for export to England.
Higher prices encouraged the cultivation of new lands and the more intense use of existing farmlands. A primary input into this increased production was the Irish peasant who was in most cases nothing more than a landless serf. Likewise, the population growth rate did slow in response to reduced levels of protectionism in the decade prior to the Famine.
This artificial stimulus to the Irish population was secure with English landlords in control of Parliament. However, English manufacturers and laborers supported free trade and grew as a political force. With the agitation of the Anti-Corn Law League, the Whigs and Tories agreed in 1845 to reduce protectionist tariffs and the Corn Laws altogether by 1849. The price of wheat plummeted in 1847 ("corn" being British for grains, especially wheat, the prime grain protected under the Corn Laws), falling to a 67-year low.
Repeal drastically impacted the capital value of farmland in Ireland and reduced the demand for labor as Irish lands converted from grain production to pasture. It should be clear that while free trade did bring about these changes, the blame for both stimulating prefamine population growth and the subsequent depopulation (the Irish population did not recover until 1951 and net emigration did not end until 1996) rests with English protectionism and the Corn Laws.