Any question answered...

Two months into our new rented house the black mould has returned again it would appear whoever decorated the last time just painted over it. Anyway we've since discovered the back and underside of the leather sofa have the mouldy shit, she is convinced it's ruined. The wall behind, it's paper is coming up and the floorboards are damp too!

We don't dry indoors
We have windows at front and back of house open a crack
No air bricks or vents anywhere
Heating on when in house - not made of money

They are dropping a dehumidifier around on Wednesday and I'm going to bleach the shit out of it, again.

How long do I wait until I phone the Environmental Health? and who buys me a new fucking sofa!

PS
Not sure I want a new sofa if its going to happen again can I break the contract and find somewhere else to live or is this only if they do nothing about it?

Is the mould emanating from an exterior or interior wall. It could be something simple like the guttering above that point is full of shit and all the rain from the roof is running off down the wall or pooling on the ground outside with nowhere to go. It will find its way in through the bricks or up under the floor. If it's an interior part of the flat then you could have a leaky pipe under the floor.
If you can track the cause down then your landlord can get it fixed before it causes any more damage for either of you. Look at your small print regards his maintenance of the place and see if there's some leverage.
A very diluted solution of bleach wiped over the mouldy bits of your sofa will kill it off and you should move it away from the damp if you can until the problem is sorted out. I doubt you'd get anything out of your landlord for the sofa yet but once you have informed him or he breaches his side of the contract you may be able to. At the very least you may be able to threaten small claims court if it comes to it.