Same day service is not available for conversion of JAR License to EASA or Issue of new EASA license. There is no need to have a UK address for the new EASA licence but as the UK will be your ' State of Licence Issue" your medical records must be held in the UK, if you had your last medical outside of the UK make sure that the records have been transferred to UK. Also check your ELP as shown on your licence is in accord with the requirements. Yes, Gatwick is very busy and priority according to need. It seems about 6 or 7 weeks guys are waiting at the moment.. I am not sure about the courier service outside of the UK! our guys from Turkey choose a " correspondence address" in UK.