I went through the process a year ago. If the UK CAA already hold your medical records, then it should be just a case of submitting SRG1136 and the required docs to Flight Crew Licencing.
It's not eligible for counter service until you receive an email from FCL saying that all their checks are done. Then you could turn up at Gatwick with your Greek licence and get the UK EASA licence issued the same day.
The process involves the UK CAA sending a "DOC 155 Request" to the HCAA to get your licence details. I would suggest making contact with the appropriate person/dept in the HCAA that deals with these requests, if you're looking for a speedy transfer.
UK FCL consider this type of application to be low priority (or they did I went through it), and was told it could take months to process. If you have a valid reason then it could potentially be expedited.
Last edited by shaftsburn; 30th June 2014 at 07:13.