The UK Supreme Court has confirmed the longstanding power of the courts to enjoin foreign proceedings that violate a contractual arbitration provision -- even in circumstances where no arbitration is on foot or in contemplation: Ust-Kamenogorsk Hydropower Plant JSC v AES Ust-Kamenogorsk Hydropower Plant LLP,  UKSC 35. The parties in that litigation had agreed to refer disputes about a hydro plant in Kazakhstan to arbitration in London. When a dispute did arise, the Kazakhstan government obtained an order from a court in that country declaring the arbitration clause invalid. (There may be a Borat joke to make here, but we won't go there.) The respondent LLP applied to the English courts for a declaration that the clause was valid and a stay of the proceedings in Kazakhstan.
The Commercial Court concluded that it was not bound to follow the foreign court's determination on the validity of the clause and that it could enjoin those proceedings, and this has been upheld by the Supreme Court. Arbitration agreements give rise to a 'negative obligation' to refrain from commencing proceedings other than in the forum specified in the arbitration agreement, and the English courts have the inherent jurisdiction to enforce this, 'independently of the existence or imminence of any arbitral proceedings'. The Arbitration Act 1996 does nothing to take that power away.