So an update on my situation and I hope to get some more advice from people again!
The dogs now seem to have left the building, the whereabouts I am not too clear but the cats still sound like they are inside. So the noise issue is now pretty much gone but the smell is still there. We met briefly with the neighbour who has confirmed he has moved and so will his animals...however the smell will not subside as it is within the walls, floors, etc. 17 years of filth. He has said he plans to have maintenance work done, ie stripping the entire flat which will inevitably bring noise and further nuisance till the end of our lease.
Due to this we stopped paying our rent this month and the landlord threatened legal action. She would not reduce the rent to a fair amount so we informed her to keep the 2 month deposit and we vacate the flat at the end of May. She then agreed to let us leave early but under the condition that we leave mid May for no other reason than she was trying to be difficult. We refused and now she has sent through a legal letter by email. As per most of the advice I received on here, I wasn't expecting her to go through with this. Please can anyone advise what should be our next plan of action??