The Court of Appeal has recently considered this rule in two cases and permitted cases to be re-opened under its jurisdiction that is very rarely exercised.
In UCP Plc -v- Nectrus Ltd the Court considered the tests that were comprehensively set out in Municipio de Mariana -v- BHP Group Plc last year namely:-
The principles applicable to applications to re-open under CPR 52.30
57. Paragraph 1 of CPR 52.30 provides: “The Court of Appeal or the High Court will not reopen a final determination of any appeal unless— (a) it is necessary to do so in order to avoid real injustice; (b) the circumstances are exceptional and make it appropriate to reopen the appeal; and (c) there is no alternative effective remedy.” Paragraph 2 provides that paragraph 1 applies equally to the determination of an application for PTA.
58. CPR Part 52.30 (previously CPR 52.17) gives effect to the decision in Taylor v. Lawrence, and the jurisdiction is often still referred to under that label. As appears from Taylor v. Lawrence, the court would have such a power even if it were not the subject of a specific rule.
59. The most useful review since Taylor v. Lawrence was in Goring at - as follows: “10. The note in the White Book Service 2018 describing the scope of the rule states, at paragraph 52.30.2: ‘… Rule 52.30 is drafted in highly restrictive terms. The circumstances described in r.52.30(1) are truly exceptional. Both practitioners and litigants should note the high hurdle to be surmounted and should refrain from applying to reopen the general run of appellate decisions, about which (inevitably) one or other party is likely to be aggrieved. The jurisdiction can only be properly invoked where it is demonstrated that the integrity of the earlier proceedings … has been critically undermined. … .’ 11. We would endorse those observations, which are justified by ample authority in this court. The relevant jurisprudence is familiar, but the salient principles bear repeating here. 12. Giving the judgment of the court in In re Uddin (A Child)  1 WLR 2398 [“Re Uddin”], Dame Elizabeth Butler-Sloss, the President of the Family Division, observed that the hurdle to be surmounted in an application to re-open under CPR 52.17 (now CPR 52.30) was much greater than the normal test for admitting fresh evidence on appeal. She observed (in paragraph 18 of her judgment) that the Taylor v Lawrence jurisdiction ‘can in our judgment only be properly invoked where it is demonstrated that the integrity of the earlier litigation process, whether at trial or at the first appeal, has been critically undermined’. And she added this (in paragraph 22): ‘22. … In our judgment it must at least be shown, not merely that the fresh evidence demonstrates a real possibility that an erroneous result was arrived at in the earlier proceedings (first instance or appellate), but that there exists a powerful probability that such a result has in fact been perpetrated. That, in our view, is a necessary but by no means a sufficient condition for a successful application under CPR r.52.17(1). It is to be remembered that apart from the requirement of no alternative remedy, “The effect of reopening the appeal on others and the extent to which the complaining party is the author of his own misfortune will also be important considerations”: Taylor v Lawrence  QB 528, para 55. Earlier we stated that the Taylor v Lawrence jurisdiction can only be properly invoked where it is demonstrated that the integrity of the earlier litigation process, whether at trial or at the first appeal, has been critically undermined. That test will generally be met where the process has been corrupted. It may be met where it is shown that a wrong result was earlier arrived at. It will not be met where it is shown only that a wrong result may have been arrived at.’ 13. In Barclays Bank plc v Guy (No.2)  1 WLR 681 [“Barclays v. Guy”] Lord Neuberger M.R. said (in paragraph 36 of his judgment): ‘36. … If a party fails to advance a point, or argues a point ineptly, that would not, at least without more, justify reopening a court decision. If it could be shown that the judge had completely failed to understand a clearly articulated point, it is possible that his decision might be susceptible to being reopened (particularly if the facts were as extreme in their nature as a judge failing to read the right papers for the case and never realising it). … .’ 14. In Lawal v Circle 33 Housing Trust  EWCA Civ 1514 [“Lawal”], Sir Terence Etherton, then the Chancellor of the High Court, summarized the principles relevant to an application under CPR 52.30 (in paragraph 65 of his judgment): ‘65. … The following principles relevant to [the] application [of CPR 52.17, as the relevant rule then was] to this appeal appear from Re Uddin (A Child) … and Guy v Barclays Bank plc … . First, the same approach applies whether the application is to re-open a refusal of permission to appeal or to re-open a final judgment reached after full argument. Second, CPR 52.17(1) sets out the essential pre-requisites for invoking the jurisdiction to re-open an appeal or a refusal of permission to appeal. More generally, it is to be interpreted and applied in accordance with the principles laid down in Taylor v Lawrence … . Accordingly, third, the jurisdiction under CPR 52.17 can only be invoked where it is demonstrated that the integrity of the earlier litigation process has been critically undermined. The paradigm case is where the litigation process has been corrupted, such as by fraud or bias or where the judge read the wrong papers. Those are not, however, the only instances for the application of CPR 52.17. The broad principle is that, for an appeal to be re-opened, the injustice that would be perpetrated if the appeal is not reopened must be so grave as to overbear the pressing claim of finality in litigation. Fourth, it also follows that the fact that a wrong result was reached earlier, or that there is fresh evidence, or that the amounts in issue are very large, or that the point in issue is very important to one or more of the parties or is of general importance is not of itself sufficient to displace the fundamental public importance of the need for finality.’ Sir Terence Etherton C went on to say (in paragraph 69): ‘69. … [The] appellants’ reasons for re-opening the application for permission to appeal Judge May’s possession order amount, on one view, to no more than a criticism that Arden LJ’s decision to refuse permission to appeal was wrong. That is not enough to invoke the Taylor v Lawrence jurisdiction.’ 15. For completeness, there should be added to that summary of the principles in Lawal the requirement that there must be a powerful probability that the decision in question would have been different if the integrity of the earlier proceedings had not been critically undermined.”
60. The Court of Appeal (Sir Keith Lindblom SPT, Coulson and Andrews LJJ) revisited CPR 52.30 in R (Wingfield) v. Canterbury City Council  EWCA Civ,  1 WLR 2863 (“Wingfield”), on the basis that “the clear message of [Goring] has still not been understood”. At , five principles were extracted from the authorities as follows: “(1) A final determination of an appeal, including a refusal of permission to appeal, will not be reopened unless the circumstances are exceptional (Taylor v Lawrence). (2) There must be a powerful probability that a significant injustice has already occurred, and that reconsideration is the only effective remedy (Taylor v Lawrence, … Re Uddin). (3) The paradigm case is fraud or bias or where the judge read the wrong papers (Barclays Bank v Guy, Lawal). (4) Matters such as the fact that a wrong result was reached earlier, or that there is fresh evidence, or that the amounts in issue are very large or the point in issue is important, are not of themselves sufficient to displace the fundamental public importance of the need for finality (Lawal). (5) There must be a powerful probability that the decision in question would have been different if the integrity of the earlier proceedings had not been critically undermined (Goring…).”
61. Although that is a helpful summary, we would sound a note of caution about  in Wingfield, where the court recorded a submission that the combination of factors enumerated above “meant that in practical terms, the requirements of CPR 52.30 are ‘almost impossible’ to meet” and observed: “That may be so; but it seems to us that the difficulty of succeeding in a such an application is merely the inevitable consequence of the principles to which we have referred.”
62. Experience shows that practitioners, and even sometimes judges, can fasten on phrases like “almost impossible to meet” and use them as a short-cut to avoid analysis of the circumstances of the particular case. It is better not to put glosses on the language of the rule itself, though of course illustrative guidance based on the case-law such as that given in Goring and Wingfield is sometimes helpful.
63. At  in Wingfield, the court said this: “In our view, an application for reconsideration of a refusal of permission to appeal involves a two-stage process. First, the court should ask whether the Lord or Lady Justice of Appeal who refused permission to appeal grappled with the issues raised by the application for permission, or whether they wholly failed so to do. Secondly, if the Lord or Lady Justice of Appeal did grapple with the issues when refusing permission to appeal, the court should ask whether, in so doing, a mistake was made that was so exceptional, such as wholly failing to understand a point that was clearly articulated, which corrupted the whole process and where, but for that error, there would probably have been a different result.”
64. The claimants submitted that a judge considering an application for PTA must “grapple with” (or “engage with”)2 the issues raised. This means, in our view, that the appellate judge should address the essential points raised by the grounds and identify why in their view the point in question does not satisfy the test for the grant of PTA: cf. Wasif at . The concept of “grappling with” the issue does not connote any particular degree of detail: what is required depends on the case.