Well ... they 'sort of do' and 'sort of dont'.
The Air Historical Branch (AHB) have record cards for each individual aircraft the the RAF has ever operated, giving details of when it was received from the manufacturer (or other source), which unit it was with, when/where it went for mods, when it came back, and damage (and which cat.), and its eventual removal from the Force. (in the 1980s I did research into Canberra and Hunter loses using the cards, and all I really got was a long list of aircraft serial numbers and dates, but it allowed me to continue searching elsewhere).
They _will_ have a card for the aircraft that you are looking for, but you need to know exactly which aircraft it is first!
As far as I'm aware they don't keep a separate list of 'losses'.
When I was at the AHB it was in Old Holborn in London, but I believe (and happy to be corrected) that they are now at RAF Northolt. I was also told that they have microfiche copies of the cards at the RAF Museum at Hendon.
As for a place to start your investigations ... I would suggest that you start with local newspaper archives on the Greek Island, or maybe the Greek mainland. It would also seem likely that they would have been buried on the island, so maybe have a look through the graveyards in the local churches, look for headstones with the RAF 'wings' on them, and maybe you will find a name. There may also be some kind of memorial to the incident? Do the Greek churches have any local records for burials covereing the period in question? In all the above you're looking to find a name or names ... and you may get multiple sets of names (!).
You could try the Imperial War Graves Commision to see if they have any record of the names you are looking for, or possibly a record of graves
on the Island.