On many different levels, the British government and the European Union are working on the details around the Brexit. This will have a lot of impact on British companies and persons. And yes, perhaps Brexit will also have an impact the topic of domains and domain registrations.
Registry EURid manages the .eu and .ею extensions under mandate of the European Commission. This mandate defines that the registrant of a .eu domain must reside within the European Union. This may be a problem for certain registrants after the Brexit is effective.
The latest information that we have, is that the Commission has asked EURid to prepare domain name revocation scenarios. Note that nothing has been decided yet. EURid is in close contact with the Commission to reach a solution that is optimal for all parties.
Until further notice, British registrants will still be able to register and renew their .eu domain names. We will inform you through our newsletters if new information on the topic of Brexit and domains becomes available. You can find a formal statement from EURid on this matter on EURid’s website.
The same question applies to other registries that require a presence in the European Union, like AFNIC (.fr) and NIC IT (.it). Those registries have informed us that they will not decide anything yet before more details on the Brexit are available.