UK & Lugano: no
Thanks to Emmanuel Guinchard for the tip-off.
The European Commission is not agreeing to the the accession by the United Kingdom to the Lugano Convention on jurisdiction and the recognition and enforcement of judgments in civil and commercial matters of 2007. The Convention was applicable in the United Kingdom until 31 December 2020 due to the UK’s membership of the European Union. Since that date the UK is no longer Party to the Convention.
Accession to the Convention is limited: it is open to Members of the European Free Trade Association and EU Member States acting on behalf of certain overseas territories (Art. 70 and 71). If other States wish to accede, the unanimous acceptance by the Contracting States is required (Art. 70 and 72,3). As this is an exernal competence of the European Union (see the Lugano Opinion, 1/03 of 2006 by the European Court of Justice), the European Union should decide on the UK’s request for accession.
The European Commission’s refusal of the UK’s request is based on its assessment of the Lugano Convention’s nature as meant for States with a close regulatory integration with the EU and its view that the Hague Conventions should be used for relations between the EU and third States. Hopefully this means signature and ratification by the EU of the 2019 Hague Judgments Convention soon. Currently the Convention has only been signed by Israel, Ukraine and Uruguay and has not yet entered into force (see status).
The 2005 Hague Choice-of-Court Convention is already in force in the EU and in the UK, along with Mexico, Montenegro and Singapore. Besides these states, China, Israel, North Macedonia, Ukraine and the United States have signed but not yet ratified the convention (see status).
See the Commission’s communication.