The firm expectation is that the European Union will agree with the British Government on a transitional period, which will run from 30 March 2019 to 31 December 2020. During this period the United Kingdom will remain part of the EU, so that European trademark registrations will be valid in the UK.
The draft EU-UK agreement provides a number of important subjects for the protection of EU trademarks and designs in the UK, after Brexit:
The current European trademark and design registrations will automatically be converted into national UK trademark or design rights after Brexit. Until 31 December 2020, a trademark or design registration in the UK can therefore still be obtained by means of an EU application. If an EU application is filed during the transition period, but is still pending after December 31st, 2020, the EU application can be converted to a national UK application, within nine months. The application date of the EU application will apply.
Of course it is also possible to file a national trademark or design application in the UK.