Updated 9th May
The United Nations has the International Court of Justice. The World Trade Organization has a Dispute process including an Appellate Body. Then there is the European Free Trade Area (EFTA) court and the Court of Justice of the EU (CJEU). These are all examples of international arrangements having specific processes for dealing with disputes.
Writing in The Guardian 3rd May 2017, Helena Kennedy QC says that -
"The problem for our prime minister is that at every turn her head hits
the hard wall of law and the role of the European court of justice
(ECJ). Theresa May
has cornered herself by insisting that the UK withdraw totally from the
court and its decisions. Nobody explained to her that if you have
cross-border rights and contracts you have to have cross-border law and
regulations. And if you have cross-border law you have to have
supranational courts to deal with disputes."
Kennedy further comments - "Call it what you like, but in the end you need rules as to conduct, and
arbiters for disagreement. Even the World Trade Organisation has a
disputes court." For this reason, Kennedy says that - " .... if May does secure a deal with the EU, we will find
ourselves quietly signing up to a newly created court or tribunal, a
Whether the CJEU continues to have any role in relation to the UK remains to be seen but it is inconceivable that the UK will not be engaged with the EU post Brexit. Co-operation in numerous areas will be crucial and therefore machinery for handling disputes will be essential. It is, quite simply, unavoidable.
Helena Kennedy QC and her Wikipedia entry. Baroness Kennedy is a member of the House of Lords EU Select Committee.
Update 9th May - View of Dr Gunnar Beck:
Gunnar Beck (University of London) argues that the Court of Justice of
the EU is not impartial and should have no role to play in post-Brexit
EU-UK relations - Policy Exchange 7th May. In this article, Dr Beck also states that - " ..... as a matter of law, Britain can leave the EU without any liability for
allegedly outstanding sums under the EU budget and other EU legal
instruments. Whether or not it is politically wise for the UK to do so,
is, of course, another question."