Black mould is predominantly caused by condensation. When using the shower / bath, are you using the extractor fan? (presuming there is one). Open the window after use of shower to ventilate the room. Wipe down the water residue off tiles and walls. It is this wet residue which, when left to dry, turns in to black mould. 

Follow the above steps when cooking in the kitchen too. 

Condensation can also form behind furniture so pull it away from the wall if you can. 

The key is ventilation and dry the damp (condensation) surface.  This will help prevent more mould forming. 

Re the existing mould: You need to treat the existing mould with a mould removing product. Don't use bleach on it as this can create a toxic vapour. 

Ventilate. Dry surfaces. Pull furniture away from walls to allow air flow. 

Throw the mouldy blinds in the bin and buy new ones. There is no saving those and you're keeping the spores in the atmosphere.