I have one of the rheumatoid types of arthritis, along with various connective tissue/joint pains. I'm prescribed the lower dose of cocodamol, but only take it last thing at night, at times of need. It helps me to sleep, though the pain will wake me, I find I can get back off to sleep, whereas paracetamol doesn't work so well for me when the pain is grim. If I take it for a wee, even at that level of 2 at night, I have to up my fibre and veg. I was first prescribed it post op, needed it for 4 days, bit as soon as the pain was manageable I stopped taking it. As elegran says, it's related to morphine and has similar effects. It's also addictive, hence my attempts to limit my consumption. My GP says you can take it alternate with paracetamol, or take 1 paracetamol with the co codeine.
I think co proxamol is no longer prescribed. Many of the people I know with similar conditions to mine, found co prox easier to take, as I did. Evidently, it was being used in suicide attempts, and prescriptions were stopped in recent years.