Is there such a a thing as a single European pilot's license? The pilot licensing process in Europe seems to be rather, well, complex... I've heard of JAA, JAR-FCL and now apparently EASA licenses, although EASA's website says otherwise:


  the Agency is not authorised to issue pilot licences and therefore
  there will not be any EASA pilot licence in the future


And on top of that, individual countries can issue their own licenses (or at least ratings) that may not be valid in other countries.

So is there any such thing as a single European (EASA) pilot's license? What I mean by that is a single license that allows a pilot to operate any European registered aircraft in any European country, e.g a UK pilot flying an F-registered (French) aircraft in Germany?

There's some overlap with this question, but the answers there don't cover the practical use of a single pilot's license throughout Europe in the way I described.

EDIT: to clarify some comments, by "Europe" I mean EASA member states (let's keep it simple); and I'm asking about pilot licensing in general regardless of the type of flying. If there's any difference in where private/commercial/ATP license holders are allowed to operate in Europe that would be interesting to know.
Is there ... a single license that allows a pilot to operate any European registered aircraft in any European country,


Yes.

According to the UK CAA
an EASA Part-FCL licence can be used to fly any EASA aircraft in any EASA member country.

I have interpreted your "Europe" as "EASA member" in order to avoid ambiguity about Switzerland, Croatia, Kalingrad, etc.


  Most aircraft in Europe are EASA regardless of state of manufacture or registration.





  The UK currently grants several levels of licence:  
  
  
  UK National Private Pilot Licence (NPPL) 
  UK Private Pilot Licence (PPL) 
  EASA Part-FCL Light Aircraft Pilot Licence (LAPL) 
  EASA Part-FCL Private Pilot Licence (PPL) 
  EASA Part-FCL Commercial Pilot Licence (CPL) 
  EASA Part-FCL Airline Transport Pilot Licence (ATPL)