That's all very, very dependent on what kind of appointment you're trying to get.

Want to see my GP/family doctor? 1-2 days, same day if it's an emergency.

ENT? Month or two at most usually, unless it's a super busy time for them. May need to go to one in another city of course.

Want to see a dermatologist? About a year, 2 at most.

Want to see a psychiatrist within the national healthcare system? No.