The other answer notes that this remains a controversial subject, and has already presented most of the evidence used by nationalist historians to make the case that the "Irish Potato Famine", or "Great Famine", was an instance of genocide.
However, it is equally important to examine the evidence that those historians tend to ignore. I will try to present some of that evidence here.
John Mitchel was many things, but he was not an historian. One of his claims to fame is that he wrote what is, perhaps, the most famous soundbite about the Irish Famine (and the one you quote in your question):
"The Almighty, indeed, sent the potato blight, but the English created the famine."
This is taken from his book, The Last Conquest of Ireland (Perhaps), published in 1860. It is worth examining the paragraph in full:
"I have called it an artificial famine: that is to say, it was a famine which desolated a rich and fertile island that produced every year abundance and superabundance to sustain all her people and many more. The English, indeed, call the famine a "dispensation of Providence"; and ascribe it entirely to the blight on potatoes. But potatoes failed in like manner all over Europe; yet there was no famine save in Ireland. The British account of the matter, then, is first, a fraud; second, a blasphemy. The Almighty, indeed, sent the potato blight, but the English created the famine."
- Mitchel, John, 1860, p219, my emphasis
So is this true?
Well, actually, no.
Yes, it is true that the potato blight devastated crops across Europe, but Ireland was by no means the only place that suffered famine. In Ireland, the famine lasted from 1845 to about 1849. The potato crop failed in the Scottish Highlands a year after the blight effected Ireland. The Highland Potato Famine would last for a decade, until about 1856.
The impact on the Scottish Highlands was less severe than that in Ireland, and the famine caused fewer deaths. In part this was because the population of the Highlands was smaller, but also – and perhaps more importantly – the impact was mitigated by aid (eventually) provided from elsewhere in the UK. This aid was provided as a direct result of lessons learned in Ireland.
Mitchel could hardly have been unaware of this. His claim that " … there was no famine save in Ireland" was clearly a lie. But, as I have pointed out, he was a politician, not an historian. Acknowledging that the potato blight had also caused famine elsewhere in the UK would have undermined his thesis that "…the English created the famine" in Ireland. Well, politicians being "economical with the truth" is nothing new!
A comment on the other answer notes that the famine was caused by "Mold growing on plants". Well, this is true. Specifically, we now know that mould was Phytophthora infestans. However, at the time of the Irish Potato Famine they did not know the cause of the harvest failure. This is a fact that is often glossed-over by modern nationalist historians.
In fact, one of the first responses to the famine by the British government was the Prime-Minister, Sir Robert Peel, setting up a commission of enquiry to try to find out what was causing the potato failures, and to suggest ways of preserving good potatoes. That commission was headed by the scientists, John Lindley and Lyon Playfair. In turn, the report from that commission was instrumental in bringing about the repeal of the 1815 Corn Laws.
In Ireland, the potato harvest improved slightly in 1847, raising hopes that the threat of famine had passed, before collapsing again in 1848 and 1849. This lead to a second period of famine. In fact, in the latter period the spread of disease probably killed more people than starvation did (although those people were undoubtedly weakened by hunger). Death from disease peaked in 1849 when there was a Cholera outbreak (the cause of cholera was also unknown in 1849).
In the first year or so of the famine, there was no reason to suppose that the Irish Potato Famine was going to be any different from the scores of famines recorded in Ireland over the previous 200 years.
Viewed in this context, some of the initial failures of the Westminster government are, perhaps, understandable. It was thought to be a short-term problem. Measures for poor-relief were supposed to have been in place since 1838. The problem would be solved when the next potato crop came in the following year.
Now, of course we have the benefit of hindsight. That was not something available to the government of the day, but some, including the nationalist historian Tim Coogan that you mentioned in the question, certainly attempt to present the series of events as if it was. This failure to present the evidence in the context of the day was one of a series of criticisms levelled against Coogan in an often ill-tempered radio debate with the historian Liam Kennedy.
Similarly, the Scottish Highlands were an agriculturally marginal area and prone to famines. Notable famines are recorded in the 1680s, the 1690s, the 1740s, the 1750s and the 1780s. However, as noted above, the response in Scotland would be conditioned by the evidence from the famine in Ireland. Nevertheless, it was estimated that three-quarters of the population of the Highlands and the Hebrides had nothing at all to eat by the end of 1846.
Religion was certainly a factor in Ireland. Yes, the British government and the majority of the population of the rest of the UK were mainly Protestant, while the victims of the Irish Potato Famine were mostly Roman Catholics. However, the problem ran deeper than that.
In the 19th century, people in Europe were much more religious than they are today. Most generally still believed that a natural disaster was somehow "God's judgement" on the victims (unless they themselves were the victims of the disaster, obviously!). An in fairness to them, we don't actually have to search too hard to find people who still express similar views today.
In the case of a disaster such as the Irish Famine, this clearly created a dilemma. How far should Christian charity be employed to counter the "judgement of the Almighty"? In this context it is worth reading the 2011 thesis The Presbyterian response to the famine years 1845 to 1855 within Ireland and in the Highlands of Scotland.
One person who's views are frequently quoted by historians (nationalist or otherwise) in the context of the Irish Famine is Charles Edward Trevelyan. He was Assistant Secretary to the Treasury during the Irish Famine, and as such responsible for government assistance to Ireland during that period. His attitudes are therefore undoubtedly relevant to any investigation of the Irish Famine.
His personal archive has been deposited in the Special Collections at Newcastle University.
In a letter to the Irish peer, Lord Monteagle of Brandon, Trevelyan expressed his opinion that:
"The judgement of God sent the calamity to teach the Irish a lesson, that calamity must not be too much mitigated",
"The real evil with which we have to contend is not the physical evil of the Famine, but the moral evil of the selfish, perverse and turbulent character of the people".
While these views are abhorrent to modern eyes – and they would undoubtedly have also been so to some of his contemporaries – as noted above, for many at that time this would have seemed quite reasonable. However, placing those statements within their historical context is not something that nationalist historians tend to dwell on.
However, notwithstanding any religious views he may or may not have held, Trevelyan was certainly not above taking advantage of "God's judgement" to achieve his own political goals. In a letter to Edward Twisleton, the Chief Poor Law Commissioner in Ireland, he wrote:
"We must not complain of what we really want to obtain. If small farmers go, and their landlords are reduced to sell portions of their estates to persons who will invest capital we shall at last arrive at something like a satisfactory settlement of the country".
In my view, it is unfortunate, and perhaps surprising, that more emphasis hasn't been placed on these opinions, rather than the more shocking (to modern eyes) quasi-religious views above, since it is statements like this that reflect the laissez-faire, free-market attitude which actually largely determined the government response to the famine.
The Government Response
This is an area where the nationalist historians arguing that the Irish Potato Famine was an instance of genocide are notoriously reticent. There is a tendency to simply quote from Trevelyan's letters and create the impression that this was the sum of the government response. In fact this was not the case.
As we saw above, the first response of the government was the commission of enquiry established by Sir Robert Peel to determine the cause of the failures of the potato crop. One outcome of that enquiry was the repeal of the 1815 Corn Laws. But this way by no means the only response.
Fin Dwyer, creator of the Irish History podcast, provided a brief summary of the main responses by the Westminster government to the Irish Potato Famine in a Reddit AMA. He identifies 4 key reactions which I quote in full here:
In 1845 most historians acknowledge that serious efforts were made by the prime minister Sir Robert Peel (Conservative Party) to alleviate famine. In secret he imported 100,000 of grain. This was intended to be used the following year to control prices. It was carried out in secret because it was known that private merchants would not import into a market they knew the government was going to partially control.
This was relatively effective (Christine Kinealy has argued this was only the case because they over-estimated the extent of the crisis).
The following year the crisis deepened with a second failure of the potato crop. However an election in the summer deposed the Tories and brought the Liberal Party to power. As advocates of Free Trade, they massively scaled back imports of food and moved famine relief in another direction.
They organised massive public works programmes so the poor could earn money to buy food. This was disastrous. The work (often pointless infrastructural projects) was too hard and wages to low to buy enough food to survive.
The cost of pubic works was enormous and reached nearly 1 million pounds per month in early 1847. This combined with the fact it was a total failure saw them temporarily adopt a third policy.
In 1847 they opened soup kitchens and although widely criticised they did massively reduce deaths during the summer of 1847.
However in September of 1847 they instituted a fourth major change where famine relief now was put on to poor law unions. Poor Law Unions were the equivalent of local social welfare administrations that ran workhouses in Ireland and were funded by local property taxes. The idea was rooted in the prevalent idea in England that ‘Irish property should pay for Irish poverty’.
These responses illustrate a sequence of changing government policies which, ineffective as we now know they often were, were clearly a series of attempts to tackle the problems created by the famines in Ireland.
These policies make no sense if the goal was genocide, and so it is no surprise that they tend to be ignored or, glossed over by nationalist historians who want to make that argument.
As you note in the question, most modern historians tend to view the evidence as a whole, and so do not accept the idea that the Irish Famine was an instance of genocide. This modern view prefers to employ Hanlon's Razor:
Never attribute to malice that which can be adequately explained by incompetence.
to that evidence, and generally concludes that the government did not intend the deaths that resulted from the famine. This was not an example of genocide.
That said, the UK government in Westminster could, and should, have done more to counter the effects of the famine in Ireland. The historical evidence suggests that their failure was the result of a toxic mix of ideology, incompetence and religion.
In short, the famine was not created by the English, but the governments of the day certainly failed in their efforts to tackle its effects.