It is the DfT, not the CAA, which has to invoke the necessary flexibility clause of the Basic Regulation to extend the Art. 12(4) derogation.
But whereas the EC and EASA are content for a 2 year extension to the derogation, which would permit FAA licence holders to fly EASA aircraft for private purposes without needing a Part-FCL licence, it seems that the DfT may decide to gold plate this and restrict the extension to 12 months....
As for those whingeing about remaining within EASA after the UK leaves the EU thanks to the dim-witted 'exit' voters who believed that blustering bag of wind Boris, just remember that any other option (such as moving legislation back to Gatwick and Westminster) would certainly increase your costs due to the need to re-employ staff no longer required since EASA took over...