In a nutshell. The conversion process from a UK licence in order to gain an EASA licence is the same as converting any other ICAO 3rd country PPL licence to EASA now. If you have more than 100hrs TT then you are required to gain an EASA Medical, English Language Proficiency test and take the Air Law and HPL Exams. Training as required to pass the skill test which may be nothing at all if you are familiar with the local procedures or a but of refresher training. For RT privileges you need to do the RT written exam and the RT practical test.
Your UK licence has no relevance other than being proof of holding an ICAO licence and can be maintained as it was before so you have two licences.
You are not able to fly an EU registered aircraft on a UK licence. Some states will issue a temporary validation which is valid for a year based on your UK licence in order for you to continue flying while you do the conversion. It can be renewed once only at the discretion of the issuing stated for a further year.