You might first need to consider what
type of painkiller your need.
Pain is often caused by inflammation, so it makes sense to try to deal with the inflammation rather than just blocking the pain. NSAIDs (non-steroidal anti-inflammatory drugs) are best for that. They include aspirin and ibuprofen.
However some forms of pain aren't caused by inflammation. Taking NSAIDs in such cases won't do much, if anything, to suppress pain. You need to take something that blocks the transmission of pain, such as codeine. (However codeine doesn't usually work well on its own; it's best combined with other drugs, such as paracetamol).
Start here:
http://www.nhs.uk/Livewell/Pain/Pages/Whichpainkiller.aspx
and then ask your pharmacist for the strongest type of painkiller for your particular type of pain. It may well be something like Paramol
http://www.nhs.uk/medicine-guides/pages/MedicineOverview.aspx?medicine=Paramol%20tablets
but, as I've stated, it would depend upon the type of pain.
Chris