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The local council and housing association don't have to give you a flat or house or rent.
Mould can be prevented with good ventilation, always leave a window or 2 open even all year round. Never get cheap tumble dryers get condensers.
There is good mould removal, but you need to put in a lot of elbow grease, then you need to paint the property with anti-mould paint. If you want a job doing, do it yourself.
I have lived in a grotty and mouldy flat, with mice but with a lot of effort, time, some expense it was sorted.