But the document you quote says " the other flat" have you got hold of a head lease for the whole building? What is the demise set out in the lease?
I was going to PM and say send me the lease, all personal information deleted, to have a look, but your profile has "turned off private messages", happy to try.
Based on the information posted, I offer my thoughts.Any action you then take is your liability. While commending individual effort, there is no substitute for a thorough review of documents and facts by paid for professional advisers