Thank you all for the informative replies.
For the benefit of others who might have the same question, I will summarize the information below.
=> The CE marking means “Free Circulation in the European Territory” – as such, if your device is CE certified it may freely enter the EU market (UK included of course).
=> You need to take care that the Labeling, Instructions for use (IFUs) and other information which are accessible to the potential users in the UK will be in the language of the relevant member state the device is to be sold in - English of course is the required language in the UK.
=> The mention of the EC REP is obligatory as a means for the European Authorities to contact your Authorized Representative in Europe.