As of 1 January 2021, any product sourced from any EU/EEA country is classed as an import in the same way as a product sourced from the US, China, or Australia as examples.
Any product coming from outside of the UK is an imported product. Under the UK Cosmetics Regulations, the importer is automatically identified as the RP. As such, you have the responsibility for full compliance of the cosmetic product, including compliance with the formulation, safety, manufacturing, notification, documentation, labelling, claims and market surveillance requirements. For more information, please check the CTPA Guide ‘Supplying Cosmetic Products on the UK Market’.
However:
Importers will also need to visit HM Revenue and Customs for information about what is required to fulfil their customs obligations.