长难句分析：
To put it simply, Prime Minister, certain informal discussions took place involving a full and frank exchange of views, out of which there arose a series of proposals which proved to indicate certain promising lines of inquiry, which, when pursued led to the realisation that the alternative courses of action might, in fact, in certain circumstances, be susceptible of discreet modification, leading to a reappraisal of the areas of difference and pointing the way to encouraging possibilities of compromise and cooperation which, if bilaterally implemented with appropriate give and take on both sides, might, if the climate were right, have a possibility, at the end of the day, of leading, rightly or wrongly, to a mutually satisfactory resolution.
主语：certain informal discussions
谓语：took place
结果状语：out of which there arose a series of proposals
主句：Certain informal discussions took place, out of which there arose a series of proposals.
定语从句：involving a full and frank exchange of views，修饰 certain informal discussions，解释讨论内容涉及“完全坦率的意见交换”。
定语从句：which proved to indicate certain promising lines of inquiry，修饰 a series of proposals，表示这些建议表明了“某些有希望的研究方向”。
定语从句：which, when pursued, led to the realisation that the alternative courses of action might, in fact, in certain circumstances, be susceptible of discreet modification，修饰 certain promising lines of inquiry，表示当这些研究方向被追寻时，意识到“替代方案在某些情况下可能会被谨慎地修改”。
非限制性定语从句：leading to a reappraisal of the areas of difference and pointing the way to encouraging possibilities of compromise and cooperation，修饰前面的内容，表示“重新评估分歧领域，并指明了妥协与合作的鼓舞人心的可能性”。
定语从句：which, if bilaterally implemented with appropriate give and take on both sides, might, if the climate were right, have a possibility, at the end of the day, of leading, rightly or wrongly, to a mutually satisfactory resolution，修饰 encouraging possibilities of compromise and cooperation，表示这些妥协与合作的可能性在适当的情况下最终可能导致“双方满意的解决方案”。
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