UK Landlord Forum / Life

I have a  flat with a very dirty neighbour who lives beneath me. Because he lives in such squalor we constantly have a very big problem with mice infesting our flat.
I have tried the council, social services, and finally the company that own the leasehold. Clearly my neighbour is breaching his lease by not keeping his property as it should be kept according to the lease. Nobody will take any responsibility to rectify this situation, which has become a major health hazard to me and my family.
The company that own the lease have told me it's not their problem and that I should seek legal advice.
Can anyone help and point me in the right direction PLEASE!