On 8 April 2020, the UK submitted its application to accede to the 2007 Lugano Convention on jurisdiction and the recognition and enforcement of judgments, in accordance with the UK government's previous statements of intention.
Lugano currently applies as between the EU (including the UK, until the Brexit transition period comes to an end - most likely on 31 December 2020 if the UK government's recent statements on the point are taken at face value) and EFTA countries Iceland, Norway and Switzerland. The UK's involvement in Lugano will however cease at the end of the transition period unless the UK accedes in its own right.
If the UK were to accede to Lugano, assuming no other agreement on jurisdiction and enforcement of judgments is concluded between the UK and the EU, Lugano would then apply as between the UK and the EU (as well as between the UK and other signatories). The result would be that there would be little change from the current regime in relation to jurisdiction and enforcement, so that English court judgments would continue to be readily enforceable throughout the EU and in EFTA countries, and English jurisdiction clauses would largely continue to be respected by those countries, and vice versa. (The Lugano Convention does have some disadvantages compared to the current regime, as it does not include the improvements made when the Brussels Regulation was "recast" for proceedings commenced from January 2015, as outlined here - but in broad terms the provisions are similar.)
The wrinkle, however, is that the UK will be able to accede to Lugano only if it has the unanimous agreement of the contracting parties - namely the EU, Denmark as an independent state (it has an “opt-out” of justice and home affairs matters under relevant EU treaties), Iceland, Norway and Switzerland. While Iceland, Norway and Switzerland have indicated their support for the UK's accession, the EU's position is not yet clear. It has recently been reported that the Commission at least may be less welcoming - in particular given that all current signatories are part of the EU’s single market or substantially participate in it, but the UK has said it intends to leave the single market once the transition period comes to an end.
If the UK does not accede to Lugano, the position regarding enforcement of English judgments and the effect of English jurisdiction clauses will depend, in part, on whether the 2005 Hague Convention on Choice of Court Agreements applies (assuming the UK accedes to that Convention from the end of the transition period - which it can do without the consent of the EU or any other contracting party). Otherwise, questions of jurisdiction and enforcement as between the UK and the EU will depend largely on local rules in each country. See this blog post for more information.
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