I have to convert my licence to EASA before I can renew them,
You do not have to convert a JAA licence, it is deemed to be an EASA licence, you just need to have it reissued in the new format. You do not have to have it reissued before you pass a ME prof check and IR however; that will require a Certificate of Course Completion from an ATO.
If your FI is current it will remain on your licence, if it has expired it will go on the back and you will need an Assessment of Competence plus a Seminar to renew it. Again you can do this before having your licence re-issued.
Under EASA, a non UK Examiner cannot sign for your SEP revalidation by experience, so don't ask, find a UK Examiner or now a UK FI with FCL-945 privileges, to do your hour with an instructor and sign you off.