The government has posted their guidance on what will happen is there is no Brexit deal:
https://www.gov.uk/government/publications/travelling-with-a-european-firearms-pass-if-theres-no-brexit-deal/travelling-with-a-european-firearms-pass-if-theres-no-brexit-deal
https://www.gov.uk/government/publications/travelling-with-a-european-firearms-pass-if-theres-no-brexit-deal/travelling-with-a-european-firearms-pass-if-theres-no-brexit-deal