How does single-sided deafness affect the different pilot licenses?
If you were willing to travel to the US (which is not all that uncommon to get a pilots license) and get your license under the FAA regulations you could do it as per the regulations,  


  §67.305   Ear, nose, throat, and equilibrium. Ear, nose, throat, and
  equilibrium standards for a third-class airman medical certificate
  are:
  
  (a) The person shall demonstrate acceptable hearing by at least one of
  the following tests:
  
  (1) Demonstrate an ability to hear an average conversational voice in
  a quiet room, using both ears, at a distance of 6 feet from the
  examiner, with the back turned to the examiner.
  
  (2) Demonstrate an acceptable understanding of speech as determined by
  audiometric speech discrimination testing to a score of at least 70
  percent obtained in one ear or in a sound field environment.
  
  (3) Provide acceptable results of pure tone audiometric testing of
  unaided hearing acuity according to the following table of worst
  acceptable thresholds, using the calibration standards of the American
  National Standards Institute, 1969:


The way this is written if you can score at least 70% in one ear on the audiometric speech discrimination test you should be good to go. Note this is for a class 3 medical with will not allow you to fly commercial operations. I am not sure how the new basic med requirements fall into all this but your best if you have specific questions is to contact an AME directly. 

From a practical standpoint, the cockpit of most small planes is fairly defining already and the headsets take mono signals from the radios so I don't really see how the lack of binaural hearing would present any issue.