Update 16 May 2018 Vedanta have been given permission to appeal to the Supreme Court.
I reviewed the High Court’s decision in Lungowe here. In  EWCA Civ 1528 the Court of Appeal has now confirmed jurisdiction against the non-UK based defendants on largely the same, if slightly more structured and expanded arguments as the High Court. (Per Owusu, jurisdiction against the UK-based defendant is undeniable; the non-UK defendants need to be joined on the basis of residual English conflicts law).
Ekaterina Aristova has analysis of Simon LJ’s leading judgment here – I am happy to refer. Of particular note is the much more reserved approach of the Court of Appeal on the merits issue of the claim. As I noted in my review of Okpabi v Shell at the High Court, in that case Fraser J looked in serious detail into the issue of merits: not, I believe, justified at the jurisdictional stage. Appeal against Fraser J’s finding will be heard by the Court of Appeal.
European private international law, second ed. 2016, Chapter 8, Headings 184.108.40.206., 8.3.2