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As mentioned, the position regarding international arbitration has not changed as a result of Brexit. The following discussion is included by comparison with the new position as regards court litigation.
Yes. The EU/EFTA courts should not hear claims brought in their courts in breach of an agreement to arbitrate in England. If they do, an anti-suit injunction may now be obtained from the English courts (again, subject to the discretion of the judge).
166 of the 193 United Nations Member States have adopted the New York Convention on the Recognition and Enforcement of Foreign Arbitral Awards 1958. This convention obliges the contracting countries to recognise arbitration awards as binding and to enforce them in accordance with their national rules of procedure.
In practice, this means applying to the national courts for recognition and enforcement of the award. There is a narrow list of defences available for resisting enforcement.