If you completed the exams with the UK CAA, those exams are no longer EASA exams. This is what's really amazing of this whole issue. The same for your medical, if held with the UK CAA, it's no longer an EASA medical.
At the moment one of two ways of getting an EASA licence holding a UK licence is to go through the ICAO conversion process which involves:
- Re-doing all the EASA exams
- Re-doing an INITIAL Class 1
- Assessment by an ATO with training as required
- Re-doing the skills tests for CPL and IR.
The other way is to get a US licence and make use of the US-EU bilateral agreement. Not sure what this involves.