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Yes, although the English courts have a discretion whether to grant this relief (known as an ‘anti-suit injunction’).
Yes (irrespective of when the clause was entered into).
This will depend on the national law of these countries (whenever the clause was entered into) and local advice should be taken. However, it is likely that such clauses will continue to be recognised.
If proceedings are started before 1 January 2021, the rules under the recast Brussels Regulation will apply (the default position under the regulation is that defendants should be sued in their home country, but there are various exceptions). If proceedings are started after 1 January 2021, national rules will apply.
It may take longer, and cost more, to enforce judgments both in England and the EU/EFTA than under the Brussels Regulation regime. (Norway has entered into an agreement with the UK for the reciprocal enforcement of judgments between the 2 countries).
It might do, because service of the claim form on the EU defendant will have to be carried out under the Hague Service Convention. Where possible, this issue can be avoided by agreeing in your contract that service can be carried out in England on English solicitors or an English service of process agent.