sammy i used to own a house that sounds similar to yours- roof with a gully down the middle which meant a big mouldy stripe down the middle in the winter! I owned the house for 10 years…had loads of work done to ensure damp wasn't getting in, which just left the condensation. I now rent a really 'nice' house which also has condensation so I'm well versed in it. Condensation causes trickle marks down the walls…warm moist air rises, hits cold air on the walls/ceiling and then turns in water and runs down. You can tell if the roof etc is leaking as it will leave a brown stain on the ceiling etc rather than condensation/black mould being the first thing you notice (I had to get the roof replaced as it was actually leaking…then afterwards I found that the condensation could actually form on the ceiling and drip off…which made me panic that the roof was leaking again until I learnt how to tell the difference).
Do you have a decent dehumidifier? If not, do whatever you need to to obtain one. My landlord provides one here that we run on low overnight…maybe the housing association can be persuaded? I was told by a damp company (who confirmed I'd got rid of all the damp) that I needed to make sure that the heating was fairly steady and to try to get the windows open to change the air daily, and not to dry clothes on the radiators, and to get a dehumidifier. The condensation did improve a lot after we bought a dehumidifier, even more when we got the tumble drier- but again, that's expense unless you can get one on free cycle.
Unfortunately bleach is completely necessary over the winter…that dettol mould remover/astonish mould remover rather than just plain old bleach. I go around the problem areas every couple of weeks at least Curtains need to be washed really regularly in the winter there is just no other way round it. Also it helps if you can ensure that furniture is away from the walls.
Do you have wallpaper? As that seems to hold the mould (it grows behind it, as I discovered). Apparently paint is better. Sometimes, if it has got really bad, you will need to get the old stuff off…paint/wallpaper/whatever and redecorate.
Also, has your housing association ensured that you have a properly functioning extractor fan in both the bathroom and the kitchen/extractor hood? As they are essential.
I wouldn't worry too much about chucking away stuff. I had mould that kept growing on my sofa 8-10 years ago. I've still got the sofa, and it hasn't come back, sofas don't smell etc, and we still have the wooden furniture that had mould on it before we got it under control, still have loads of my old clothes. My 3 kids all lived in that house, and none of them have health problems/asthma despite all my fears, and us living in the middle of a city.
You might have tried all of the above already, but it is funny how little changes can make a massive differences. I leant my house to a friend before it was sold, and she clearly didn't open the windows or use the dehumidifier and I was shocked by the amount of mould that I had to clear off the walls when I went back to the house!
I lived in an area where lots of us had 'mouldy' Victorian teeny houses and we used to have a right moan all the way throughout winter. It helps to have other people who are in the same boat as it gives you that reassurance that actually it'll be ok in the end.