Black mould also goes by the names Stachybotrys chartarum, S. atra and "toxic mould." It gets a lot of press for its toxin-producing spores, but according to the CDC, black mould "should be considered the same as other common moulds...." The CDC further states that a link between Stachybotrys and rare health conditions is unproven. Harvard toxicologist Ronald Gots attributes toxic mould's reputation for causing "sick building syndrome" to the hype of mould remediators who profit more from fear than from science. With this perspective, you should clean black mould from walls no differently than other moulds.
Repair any leaks or other source of moisture. You don't want your hard work immediately undone with another infestation. Also clean up pooled water, fix any broken sump pump and repair any cracks to the outside.
Cut out a small piece of the wall where the mould has penetrated (e.g., with a hand saw or jab saw). Make the hole in the wall large enough to see inside with a flashlight. If you see mould inside, you may have to just take down all the drywall, clean everywhere and put up all new walls. Otherwise, continue with the next step.
Inspect the piece you cut out for depth of mould penetration. If it has grown more than a quarter-inch deep, your cleaning solution won't necessarily soak in enough to kill it all. You'll have to cut out all the mould-infested drywall you see and use spackling paste and a smoothing spatula to insert new sheets, which can be purchased in various sizes at a hardware store. If the penetration is shallow, go to the next step.
Mix a half gallon of 10 per cent hydrogen peroxide (H2O2) and a cup of boric acid. (The 10 per cent can be made by watering down 35 per cent H2O2, which is easier to find in stores.) Don't use the 3 per cent H2O2 in drugstores; it's not a strong enough antiseptic. Light exposure turns H2O2 into water, so make no more solution than you'll use in four hours.
Soak the mould with the solution thoroughly. Scrub only as deep as the mould is soaked: you don't want to disturb dry spores and send them airborne. This would make you sick while working and start a new infestation in the room. Keep soaking the mould regularly while scrubbing away.
Soak the wall thoroughly after the mould is all scraped away, just to kill what you can't see. As soon as possible, apply spackling paste and smooth it with a long spatula to regain a flat surface. This will hold any spores in place. Prime it and paint it for added protection from remaining spores.
Mix a cup of liquid bleach with a gallon of water to wash mould off a limestone wall. Use a pressure washer, if you can get one---but not for limestone roof shingles, which need gentler treatment.
Keep wetting the wall with the solution for half an hour. Use a face mask and goggles to reduce the bleach's affect on you. If you're working indoors, open the windows to ventilate the bleach fumes so you can get through the job with minimum irritation.
Use soapy water to wash away the bleach.
Use goggles and gloves to apply the boric solution. Keep a pail of water handy in case you get any in your eyes or on your skin. Use a disposable face mask if the scrubbing will take more than a few minutes, to protect yourself from hay-fever symptoms caused by the mould.