The Law Society, the Solicitors Regulation Authority and the Bar Council have expressed their Brexit concerns in their responses to the Justice Committee's inquiry. Those concerns include that the UK (and in particular, London) will lose its position as the leading centre for dispute resolution, that UK lawyers will lose their rights of audience before EU courts, lawyers' legal and practical abilities to advise clients based within the EU and again, rights of enforcement.
A key focus for litigation lawyers will be jurisdiction, choice of law and the recognition and enforcement of domestic judgments within the EU. It is the Recast Brussels Regulation which provides for the current regime but there is considerable uncertainty about what regime will apply post Brexit. Will the Regulation be adopted in its existing form? Will another convention be adopted or nothing at all? Much depends on the Government's own decision making during and after the Brexit negotiations.
If your case is not heard within the jurisdiction in which you reside this will substantially increase your costs (even just on a practical basis). Furthermore, it is not clear whether UK judgments will continue to be readily recognised and enforceable in other member states - so in circumstances where a defendant has assets abroad this could considerably hinder your chances of recovery. You might also no longer be able to easily serve proceedings upon a party within the EU - instead you may have to endure the further costs and delays in seeking permission to serve out.
On a wider basis, those involved in disputes could be dealing with more exporting/importing issues as disputes arise throughout the transition period and contract termination disputes should there be a prolonged weakening of the pound.