Firstly, if the IRA were 'soundly defeated' nobody told them. I dread to think what their 'winning' would have looked like if we suppose them to have been defeated.
As Wilbur has said, the reaching out began when it was obvious no one could win and involved Thatcher's and Major's governments before Blair. The British army could not kill the tiny gadfly and the IRA could not force a British withdrawal from Ireland, at least not any time soon.Like it or ...
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...not, again as Wilbur has said, the IRA were a force to contend with. Highly organized, smart and ruthless. We can admire their tenacity whilst deploring their methodologies. It is self-evident, at least to me, that, again much as we might dislike it, 'terrorism' works at some level, if only to focus minds on finding a way to end it. It finally dawned on the combatants that winning wasn't on the cards for either 'side.' , and this coincided with a helpful support from Dublin, and all sides found the willingness to make peace an option. The peace process in Ireland, as the Northern Irish poet Seamus Heaney said, was 'when hope and history rhyme.' What a wonderful viewpoint.
I also want to mention the use of the highly pejorative and loaded word ' terrorist.' This word was used by Thatcher to describe Nelson Mandela - a man most of us would hail as a saint. iIt has probably been rolled out to label countless people as a way of making them the bad guys. It often is accompanied by the a contrast with the 'security forces,' so we immediately envision the good guys with the bad eggs, and once our sense of where right and wrong lie, we can act appropriately.
But the world is not like this. This oversimplification is perfect way to hide malfeasance. The IRA are bad we can treat them however we like, the security forces are good, we must always have their backs. So, in the skewed world of Northern Ireland, the state can cooperate with loyalist paramilitaries to kill those suspected of being in the IRA extra-judicially. These loaded terms allow for all kinds of injustices such as locking up people you know didn't commit a crime, and leaving them to rot in prison (Birmingham six). The ironic thing about this is that the very injustice you thereby commit feeds the beast you want to kill, and the state, as the 'security forces' acts no differently to the 'terrorists' they seek to destroy.
On a broader comment on such labels, and again, not defending terrorism in any form, but rather attempting to understand what drives people to such extremes, it's worth noting that, as a Catholic nationalist in northern Ireland, you were very likely not to have a job or a house, or in many cases a vote, just because of who you are, and it's worth noting that the 'security forces' were almost 95% or more made up of Protestant 'loyalists.' and, the early years of the 'troubles' you might indeed well be interned without trial, just because of who you are. Not difficult to see the recipe for violence in this set-up.
On the actual topic under discussion, the reneging on an international treaty, the undermining of the rule of law undermines all law. It is obvious that no one will view the UK's word in the same light. the former UK amabassador to the US wrote a great piece in the Guardian on this. https://www.theguardian.com/politics/2020/sep/15/kim-darroch-new-brexit-bill-damaging-to-uks-international-reputation