I had a chronically damp lower ground / half basement flat. I was allocated it via the local authority bid system but it was a Housing Association flat.
I asked Environmental Health to do an inspection and they actually condemned it as unfit for habitation on numerous grounds. The HA already knew that when they moved me in, evil.
Even so, this did not help my situation much as still nobody would actually do anything. The council didn't even put me back into the bid system which was my legal right at that time. But here is what I found out about the law.
The law only means anything as much as you can enforce it. If your home is in disrepair and you can't get a solicitor to take your case against the council or HA you're pretty screwed. Maybe you can get a solicitor.
In the end I got a solicitor onto my case - a housing disrepair solicitor who took my case on Conditional Fee Arrangement (CFA) which is effectively 'no win no fee'. My HA was given a court ordered schedule of work to bring my home back into liveable standard and I was 'decanted' for 8 weeks. However, the HA never did the work and that's another long story.
Your best bets are - go to your Council Environmental Health and ask for an urgent inspection. Go to your local Councillor and write to your MP or even go to see them in person. Make sure your GP knows all of this and how badly it's affecting your health and wellbeing and mental health.
Go back on to your council website and re-register as a social housing applicant - the form will ask if you're already a tenant and on what grounds you need to be moved, this will flare an investigation into your situation and could possibly open up a fresh housing application for you so that you can try to bid for a different property.
Do use the home exchange and homeswapper sites, you never know what someone has in mind. Also depending how old you are, if you're over 55, check out whether you can apply to your local authority over 55s housing / sheltered housing / supported housing as that could be a way out of your current home. Also look at the seaside and country home or 'get out of area' schemes.
Take legal advice about whether you can commission the repair work to be done yourself and re-charge it or withhold rent to cover it (this is a rare and highly legal circumstance and must never be attempted without legally binding approval).
Attend any housing advice or legal advice drop in sessions at local community law centres or the CAB etc. If you can't find any, seek out Housing Solicitors for two things - to try and get a 'housing disrepair' case solicitor or to try and get legal backing to support your right to be re-housed. Unfortunately in the current climate this is not easy as solicitors are mostly helping people fight eviction.
In my opinion, DO NOT walk away from a council house tenancy. You could be considered 'intentionally homeless', you may risk any benefits or support you're on and you will absolutely be refused future help from the same Local Authority. You could try and speak to Shelter on this issue.
Also check out if there's any Housing Co-operatives or Housing Associations in your area that you'd be eligible to apply to directly as there are some few cases of housing organisations that actually don't operate via the Council bid systems and are their own independent bodies, especially co-operatives.