The authority that holds your medical records must be the same that issues your licence. So if you do your medical in Greece and want a UK issued licence you'll have to ask the Greek Medical Authority to transfer your medical records to the UK CAA.
I don't know the pros and cos of doing the whole process in Greece. I know that Portugal is quite cheap too, but there's more bureaucracy involved. Probably the same happens in Greece.
The UK CAA is expensive for sure, but things are very straightforward.