Wouldn't that requires huge macro-historical changes tough? As long Britain leads financially and technologically the European economy, there's little to no incitative breaking with an providentialist-smithean concept of economy.
Yes it would require significant historical change, but not quite in the way you explain I think. Or at least, more nuance is needed.
There was, as people have pointed out, relief available during the Famine, but it was not enough by any means. It is worth noting that the Famine came after a European famine. There simply weren't large piles of food lying around for the government to purchase quickly. Yes, Britain was exporting tons of food to Europe and the Americas during the famine, but action would have required compulsory purchase/seizure of stock held by merchants and farmers. This would have been very difficult to contemplate in the 1840s.
Britain was a nation wedded to free-trade, but it's more important than just that economic justification of 'free trade has made us the most powerful economy so it must be right and we need to stick to it' concept. Britain saw Free-Trade as part of its national consciousness, tied to fair dealing and the rule of law and democracy. It isn't as simple as Trevelyan being bullish about it - it would have been a HUGE step to undertake such a form of relief. Peel and others weren't being callous when they pushed for repeal of the corn law to help in Ireland, they genuinely thought that this would help.
We expect huge and dramatic things of Governments in the past with our modern-day hindsight, but for as many callous and indifferent Britons there were many others who believed what they were doing was right. Or simply couldn't summon up the strength of will to push through a truly radical solution. Think about the Migrant Crisis today. Largely, Western governments have failed when it comes to the most intense humanitarian crisis of the decade, whilst the few that took radical action, such as Angela Merkel in Germany, are now paying a political price for that step amongst those who see it as the wrong idea. Yes Britain could have done more, but it would have required deep and radical action and been a huge political risk.
To answer the OP's question about the consequences of relief:
Short Term:
*Buying up huge amounts of food, or stopping Irish food exports, or whatever interventionist steps are taken probably end up weakening Peel's Government even more than OTL.
*The Irish Poor Law, through which the relief would have been administered, is strengthened immeasurably. The Workhouse System, without administering the heavy burdens of funding emigration, continues to be the main system through which crisis and poverty is managed.
Mid Term:
*A higher population, and less buying up of absented freeholds by large landlords, changes the character of agrarian dissent in Ireland. The Irish Land War looks a little different, but I think that those rural smallholds that survive will still struggle in the 1870s downturn across Europe.
*Fewer Irish emigrate to America, with fewer pathways established by famine emigrants, but poverty and poor conditions in Ireland still push many into going.
Long Term:
*The Famine relief has little effect on the tensions over British Rule in Ireland. As OTL the majority of Ireland favours some form of Home Rule until the Easter Rising etc. Whether these events are slightly butterflied or not, I think its important to think about the long-term issues that shaped that difficult relationship rather than just find one POD.
*Famine relief will not change pre-existing ideas about the Irish in Britain [that they are feckless, lazy, and in need of charity] or Irish ideas about English rule [that it is overbearing, pauperizing, and patronizingly out of touch with the needs of Ireland more generally].