If the UK leaves the EU on 31st January 2020 with no agreement in place regarding ongoing data protection, there would be no immediate change in the UK’s own data protection laws. This is because the Data Protection Act 2018 would remain in place and the EU Withdrawal Act would incorporate the GDPR into UK law alongside it.
Furthermore, if the European Commission does not make an adequacy decision regarding the UK at the point of exit – EU partners should be given information related to the legal basis for processing and the Government have recommended standard contractual clauses, which are model data protection clauses that have been approved by the European Commission and enable the free flow of personal data when embedded in a contract.
Such standard contractual clauses are being drafted in line with that guidance (available here) and will be released prior to the deadline.