Painting over mould is the single most common mistake I see, and it never works. The spores are still alive under your fresh coat, and that ugly black bloom will ghost back through within a month or two. You have to kill it first.
Start with a fungicidal wash — most decent merchants stock one, and it's cheap. Apply it neat, leave it to dwell for the time on the tin (usually 24 hours), then wipe off. Wear gloves and a mask; mould spores are nothing to mess about with. Avoid the temptation to scrub it dry first — disturbing dry mould throws spores into the air. Wet it, treat it, then remove.
Forget the neat-bleach trick people swear by. Bleach lifts the black colour but doesn't always kill the root in porous plaster, and it leaves salts behind that mess with paint adhesion. A purpose-made fungicidal wash is the proper job.
Once it's clean and bone dry, prime the affected area with Zinsser Cover Stain or Zinsser BIN — both block any residual staining and stop it bleeding through your topcoat. This step is non-negotiable on stubborn patches.
Now the important bit: mould is a symptom, not the problem. It thrives on cold surfaces and trapped moisture — north-facing walls, behind wardrobes, poorly ventilated bathrooms. If you don't fix the damp or ventilation, you're just delaying the next outbreak.
For the topcoat, breathability helps. Earthborn Claypaint is genuinely vapour-open and a cracking choice for walls prone to condensation. In bathrooms and kitchens, reach for a proper moisture-resistant finish like Dulux Easycare Bathroom or Crown kitchen & bathroom paint, which shrug off steam far better than standard emulsion.
Colour-wise, lighter shades on a cold wall help reduce the temperature differential that feeds condensation — something soft like Farrow & Ball Cornforth White or Skimming Stone works nicely without going stark.
Sort the cause, kill the spores, prime, then paint. Skip any of those and you'll be back here next winter.