Although the UK has left the EU, companies wanting to trade with the EU will still have to ensure that their products and services are traded in compliance with EU law; which is also true for any trade with any other country in the world.
In terms of eCommerce the latest developments within the EU are:
The Digital Services Act and Digital Markets Act encompass a single set of new rules applicable across the whole EU. They will create a safer and more open digital space, with European values at its centre.
The DSA and DMA have two main goals:
The e-Commerce Directive is the foundational legal framework for online services in the Internal Market. The purpose of the Directive is to remove obstacles to cross-border online services in the EU and provide legal certainty to business and citizens.
The Directive sets out basic requirements on mandatory consumer information, steps to follow in online contracting and rules on commercial communications (e.g. online advertisements and unsolicited commercial communications).
As advised by the UK Government and the latest .eu domain name notice from the European Commission:
You can only register or hold .eu domain names if you are:
UK owners of .eu domains registered prior to the UK's withdrawal will not be able to renew them. Moreover, the registry for .eu will be entitled to revoke such domain names on its own initiative.