Update 23 09 2022 a late update on the UK procedure, triggered by a July judgment of the Luxembourg Supreme Court:
The Court of Appeal  EWCA Civ 1801 dismissed the appeal against the stay, however that was later overruled by the Supreme Court [ UKSC 5]: it lifted the stay on enforcement. The UKSC judgment discusses sincere co-operation, impact of international law on EU law procedures, etc, and the European Commission then initiated infringement proceedings against the UK.
Then, on 14 July 2022 the Luxembourg Supreme Court held the Micula award to be unenforceable, on account of Romania’s membership of the EU per 2007.
Update 3 May 2019 on 12 March 2019 the Brussels Court of Appeal replicated the High Court’s decision, and referred generally to the CJEU on the authority nay obligation of Member States to refuse to recognise awards of this kind.
I have written this blog post with in my mind a rather bibliographical purpose: having collated all sources I would rather like finding them all back again. In  EWHC 31 (Comm) Micula and others v Romania and the European Commission, the High Court effectively halted the enforcement of an ICSID award, pending a Court of Justice Ruling (in Case T-694/15) on the legality of an EC finding of State Aid. The Award arose out of the Romania-Sweden BIT and as such got caught up in the maelstrom (this could have been an intended pun however etymologically the word is Dutch, not Swedish) of discussions surrounding EU competencies in intra-EU Bilateral Investment Treaties (for background on that issue see here).
Not quite following the rabbit down the hole however nevertheless quite a wonderland of colliding legal regimes.