What license woud an ex-military aircraft (E.g, L-39) go under according to the UK-CAA, an EASA licence or a non-EASA license?
According to CAP 632


  6.1 Ex-military aircraft on the UK register with a ‘Permit-to-Fly’ may be piloted by either private or professional licence holders. Pilots must hold a current civil licence with a current civil class or type rating appropriate to the ex military type[s] being flown or where no civil type rating exists, an Aircraft Type Rating Exemption from the need to hold a type rating.
   Any questions relating to licence matters should be addressed to CAA PLD


...


  
  Any turbine-powered aeroplane - To fly an ex-military turbine-powered 
  aeroplane a pilot must hold an Aircraft Type Rating Exemption. See paragraph 
  6.7 for details of obtaining an Aircraft Type Rating Exemption
  


and so on.

Ex-military aircraft are non-EASA aircraft. Ref