Plum is regulated through its partner MangoPay.
MangoPay is based in Luxembourg and is classified by the European Commission (EC) as an e-Money provider. Being an e-Money provider means that MangoPay has the license to hold your money and follows all the necessary regulatory guidelines to do so. The money is held with Barclays Plc in the UK.
MangoPay (and many other banks and firms) has passported its license to the UK which means that the FCA has authorised MangoPay to operate in the UK. In the case of Brexit, MangoPay has taken the necessary steps and will continue to operate in the UK normally.