Has Brexit had an impact on cross border disputes?

In a word, yes, when it comes to cross-border disputes involving the UK and the EU/EFTA countries. Contracts containing an exclusive jurisdiction clause in favour of England, and resulting English judgments will in most cases continue to be recognised in the courts of EU/EFTA countries. But the regime is less comprehensive, streamlined and (in some respects) certain than that which applied until 1 January 2021.

There will still be many factors that will make English law and jurisdiction attractive options, but with arbitration unaffected by Brexit, it may be worth considering the relative merits of litigation and arbitration to resolve contractual disputes.