Update 18 May 2023 in the meantime a fresh jurisdictional challenge will be fought out as a result of BHP belatedly requesting for Vale to be brought into the proceedings, with Vale contesting jurisdiction. There issue is flagged in Municipio De Mariana v BHP Group (UK) Ltd & Anor  EWHC 1134 (TCC) where some case-management decisions were taken, too.
Update 17 01 2023 my article on Articles 33-34 has now been published: Lis Pendens and third states: the origin, DNA and early case-law on Articles 33 and 34 of the Brussels Ia Regulation and its “forum non conveniens-light” rules, The link in the title should give free access to the first 50 takers, and I assume link to the review for those that come after.
Municipio De Mariana & Ors v BHP Group (UK) Ltd & Anor  EWCA Civ 951 (background to the case here) is the appeal against the stay (and partial strike-out), on forum non conveniens, A33-34 Brussels Ia and case-management grounds ordered by Justice Turner. The Court of Appeal has overturned all three reasons for a stay. Bar appeal with the Supreme Court (which the defendants are likely to seek) the claimants may now bring their claim in the courts of England and Wales.
For the benefit of full disclosure I should add I am instructed for claimants in the case; this post however does not speak for claimants or co-counsel in the case and is merely my academic view on the judgment.
The judgment runs to 107 pages (not excessive given the issues and facts covered). There is little point in me rehashing it all (again, reference to my previous post may be useful). 40 pages are spent describing the applicable law in Brasil and the various proceedings underway there. This is of particular importance seeing as the crux of all three defences advanced is that the proceedings are already underway in Brasil and should not be duplicated by an English procedure.
In the main:
Abuse is dealt with  ff, with the key points for reversal listed  and the CA’s own analysis detailed thereafter, summarising in  ff.
Of particular note here is the rebuke of Justice Turner’s finding of ‘unmanageability’ of proceedings (which the CA as such does not believe will be the case) having dominated his subsequent findings on other elements of abuse, and the use of forum non conveniens criteria for the assessment of abuse.
 Consideration should have been made of the question of the availability of full redress in Brazil. To those following business and human rights litigation, this will be a welcome finding.  Support for manageability of proceedings not having a place in the abuse assessment (other than  if the claimant were to have vexatiously made the proceedings unmanageable himself), was found in Mastercard v Merricks  UKSC 5.
 discussion of what Turner J at the abuse level, saw as complications arising out of the existence of parallel proceedings in Brazil, already indicate the direction the Court took on the forum non and A34 issue: the many differences between the English and the Brazilian proceedings.
The Article 34 Brussels Ia application is discussed  ff and is of particular relevance to readers of the blog.
Firstly  the Court of Appeal settles for now the Privatbank /Euroeco discussion on ‘expediency’ (see also ia SCOR v Barclays) in favour of the former: What is required to fulfil A34(1)(a)’s condition is that it must be desirable for the two actions to be heard and determined together in order to avoid the risk of irreconcilable judgments, irrespective of whether that is a practical possibility. (Claimants have reserved the right to contest this should the matter go before the Supreme Court).
Further  the test of relatedness for the purposes of A34 is held by the CA to be a broad test:  per Tesauro AG in C-406/92 The Tatry, whenever the judge seized of the stay request considers that the reasoning adopted by the court hearing the earlier proceedings may concern issues likely to be relevant to its own decision, the cases can be said to be related. This is opposed to the narrow approach in the House of Lords Sarrio SA v Kuwait Investment Office  AC 32: there the HoL held that for there to be a risk of irreconcilable judgments the inquiry is limited to “primary” issues which are those necessary to establish the cause of action, and does not include issues which the court might or might not decide and which would not be essential to its conclusion.
On the condition ‘that the court of the third State will give a judgment capable of recognition‘, at the hearing the question was asked whether a twofold condition exists, namely (i) that a judgment was expected as a matter of fact and (ii) that the expected judgment was one which was capable of recognition and, where applicable, enforcement. The Court  supports the view that only the second (ii) condition applies. I do not think that is correct and I am not convinced by the Court’s travaux analysis on this point  – I detail this in my forthcoming paper in the JPIL. As for that second condition, the CA holds  that ‘the exercise at this stage is a conceptual one, looking at the type of judgment to which the third state pending action may give rise, and evaluating whether it attracts recognition, or where applicable enforceability.’
‘Necessity for the proper administration of justice’ is dealt with  ff (although it confusingly includes discussion of more than just this ultimate A33-34 condition), starting with the discussion whether a stay was available or could be justified on a “consolidation” basis (effectively, an allocation of jurisdiction , or on a “wait and see” basis [temporary case-management: wait and see whether and to what extent the outcome of the case ex-EU affects the action in the member state].  Underhill LJ takes a holistic approach: Does waiting for the outcome [of the Brazilian proceedings held to be related] give rise to advantages which sufficiently outweigh any disadvantages such that a stay is necessary?  The CA takes a broad approach to the issues that might be considered, including issues classic to a forum non conveniens analysis. I believe that is right, with the important caveat that A34 must not effectively be conflated with forum non (which is what the first instance judge had effectively done) (compare Ness).
 the Court takes a formalistic (and correct) view on the ‘related proceedings’ and their being ‘pending’:
for the purposes of the article 34 application, the nature and extent of overlap which falls to be considered when addressing whether and to what extent there is a risk of irreconcilable judgments, and in considering whether that risk weighs in favour of a stay being necessary for the proper administration of justice, is limited by reference to that which might be decided in the [pending Brazilian proceedings].
In particular, an advantage eg in winding-up proceedings viz the defendants or related undertakings, which could be obtained down the line from the outcome of the related proceedings, would not be caught by the comparative overlap and the likelihood of relatedness therefore is seriously reduced ( contrary to Turner J’s finding that that the list of areas in which potentially irreconcilable judgments are liable to arise was “almost endless”).
 ff the CA makes its own assessment of the ‘proper administration of justice’ requirement given the judge’s core mistakes (particularly, his abuse conflation and the consideration given to future proceedings which are not pending).
 The CA holds that the continuation of the claim against BHP Australia (for which later in the judgment it finds that this is not barred on forum non grounds) in and of itself argues against an A34 stay (and that relevant parts of Lord Briggs’ speech in Vedanta do not change that).
Obiter  ff it lists other factors against a stay:  there is a real possibility that final resolution of the related BRA proceedings, if they resume at all, is well over a decade away;  ‘For there to be a further delay of years, and quite possibly over a decade, before [E&W proceedings] could resume would cause very substantial prejudice to the claimants in obtaining relief, and would be inimical to the efficient administration of justice as a result of all the well-known problems which delay brings to the process’;  ff there are many disadvantages to the BRA proceedings including that these will not address the liability of the defendants in the E&W proceedings;  the degree of overlap between the proceedings is limited.
The forum non application is highly relevant given the English courts’ preponderant reliance on it, outside the BIa context, following UKSC Brownlie. Of note here is ia  the unrealistic prospect of the alternatives being suggested – I will leave the further forum non analysis to blogs less focused on European conflict of laws.
Rejection of a case-management stay is done succinctly, with Underhill LJ noting ia  that such stay would be incompatible with A34 and A4 BIa.
All in all I do not agree with each of the Court’s findings on tenets of A34, however in general the Court’s application reflects the correct approach to the Article, which very much makes a stay the exception.
See also Lis Pendens and third states: the origin, DNA and early case-law on Articles 33 and 34 of the Brussels Ia Regulation and its “forum non conveniens-light” rules