The European Commission announced that UK based companies and residents that own .EU ccTLDs will have to surrender those domain names after Brexit. The notice reads:
As of the withdrawal date, undertakings and organisations that are established in the United Kingdom but not in the EU, and natural persons who reside in the United Kingdom will no longer be eligible to register .eu domain names or, if they are .eu registrants, to renew .eu domain names registered before the withdrawal date.
This obviously has serious implications for those who have branded their companies or brands around .EU TLDs. Not only will they not technically be able to own or use the domain name for their web site, UK citizens/companies also will not be able to redirect the domain name to a .co.uk or other TLD migrated to.
In addition, this loss of domain ownership can have implications for reputation management and encourage domain squatting.
Brexit is currently scheduled for March 30th, 2019, so if you believe the European Commission will enforce this, it might make sense for .eu domain owners to consider setting up a new domain name now. This gives you time to prepare the branding and marketing around a new domain name and of course set up the 301 redirects and any impacted hreflang changes a year in advance.
It is obviously best from an SEO perspective to have 301 redirects from one URL to another URL forever but if that is impossible, the longer you have 301 redirects in place, the better off you are with Google, Bing and other search engines.
The Register reports there are about 300,000 domains under the .eu top-level domain that have a UK registrant.
You can read the full announcement in this PDF document.