Damp mouldy home and dishonest landlord

Hi all
Just wondering if anyone can help with advice. We moved into a property on 30th October. The next day we realised that there were issues with damp at the property and I started wheezing. A damp specialist came round and said there was 80% humidity and a major damp and mould issue requiring 13k in repairs.
I left the property within 3 days due to my asthma and my husband stayed in the property for 7 more days whilst we waited for the landlord to sign the end of tenancy agreement. We ended up putting our possessions in storage, in air b and bs living out of suitcases with our 3 pets until we moved into our new flat on 24th November. I was signed off sick with stress. The whole thing has cost us thousands (London!) and has been so awful.
The landlord still hasn’t signed the end of tenancy agreement. The agent says he won’t talk to us to mediate, but he will give our deposits back but not pay us back for the 1 months rent we paid, and will not reimburse us for any other costs.
In addition to the damp, the agent did not provide us with the electric safety certificate until we had moved in, which showed they were dangerous.
Never been in this situation before, we are just renting for a year as a stop gap. All my previous rentals were fine, but the agent/landlord are in this together and neither will accept any wrongdoing on their part.
I would like to take the landlord to small claims court and also complain to the property ombudsmen, mayor of London authority for rogue landlords reporting etc, but expect the agent will take out a county court injunction against us for the rent (even though they accepted the keys back)? Anyone have any advice or experience? Would be hugely grateful thank you

This all sounds so dodgy. Who paid this specialist? What problems found? What changes covered by 13k?

Hi Graham
The agent paid for the damp specialist who was from a. Legit big company. He said all needed damp coursing, all fittings needed to be removed and put back in afterwards. All the walls were damp often water running down them
Thank you

Severa rising damp found, mould, condensation. If you left a box out, picked the box up the next day, water would pour out of the box.
They have never apologised to us just try to get out of giving us any money back

You probably have a right to unwind the tenancy under consumer legislation if the landlord knew or should have known about the damp pronlem. As its within 30 days, you would also be entitled to a full refund of all monies paid, but Im not sure about compensation. You should probably speak to a solicitor in the first instance. You could also write him a Letter Before Action outlining you case and giving him a fixed period to respond. You should be aware though that if you demand a large sum in compensation, he is likely to decide to take his chances in court.