What body creates legally binding aviation regulations in Europe?
EASA regulations,  as emited by the European Council, automatically become law in all EU member states (it is part of EU adheration treaty).  

PART-FCL, for instance begins with this text:


  COMMISSION REGULATION (EU) No 1178/2011 
  
  of 3 November 2011 
  
  laying down technical requirements and administrative procedures
  related to civil aviation aircrew pursuant to Regulation (EC) No
  216/2008 of the European Parliament and of the Council


Because of the way these regulations are framed, local regulations (emited as law by local parliaments) will take precedence over regulations emited by the European Parliament, so some local authorities (I’m looking at you UK) will amend/change/adapt these regulations as they see fit.

Make no mistake, EASA regulations are law within the European Union’s member states.