In most European countries, opioid painkillers will only be administered in hospitals when pain is so strong that you can't fight it with Ibuprofen or Aspirin (e.g. after surgeries).
I don't know a single person here in Europe who got a recipe for opioids by a GP or after leaving the hospital. That's not because pain is not treated but because doctors realise how dangerous opioids are.
In the most European countries co-codamol is OTC without a prescription.
I think it's quite common to get co-codamol or dihydrocodeine from a GP in the UK. However, this is really weak in comparison to the high-dose oxy or hydrocodone that US doctors seem to prescribe.
CO-Codamol has a comparably low codeine content which would likely make it less addictive (only guessing, not a doctor). It's a prescription drug in the UK.
Will probably depend on the doctor but the GPs I have seen in the UK have preferred Ibuprofen if it can treat the pain.
I don't know a single person here in Europe who got a recipe for opioids by a GP or after leaving the hospital. That's not because pain is not treated but because doctors realise how dangerous opioids are.