How to solve this mould problem

Before I get down to details I just wannna say that we are in UK and unable to go anywhere else as of financial issues.

We've been living and renting a bottom floor flat for 4 years and it's been total nightmare. We been doing fine. Its just that the mould has gotten best of us. Before I list the rooms with problems just want to note that the house is quite old and way it was built was poorly done when looking from outside brick work. Apparently flat above us have same problem but instead the owner wishes not to fix it as it requires money and time. We also know that the roof has a leaking but we are unsure if it is the cause of it. Another thing to note that inner walls of our flat are perfectly fine but it's the outwalls that anything touch are the big problems.

For better understanding of our situation I'll list rooms and the conditions that they are in.

1. My dad bedroom is worst one of them all. there are 3 outer walls that are damp and have mould at bottom of them. We've tried everything to get it fixed such as Bleach or allowing some air to flow through.

2. My bedroom has 2 outer walls and 2 inner walls. The 2 outer walls are fairly wet sometimes but show no signs of mould.

3. Living room/ lounge has 2 out walls that are wet also.

4. Kitchen is unsure but there has been signs of mould on things such as dining chairs.

I read a post on this site about people suggesting to get anti-mould paint and some sort of spray to stop it or keep it at bay. Knowing this is great because I didn't know there was such a thing, but problem is still there as it catches onto things and just destroys it. Today I wanted to listen to music but when I open the case my headphone with leather padding were covered in mould. I understand it is bad for our health but having no where to go or if we did it would be a struggle.