While arguably the contractual tenancy ended and a new statutory one started, it is the same underlet, and as it is open ended severable on two months notice, the reply to the agent is simply that this is simply a statutory continuation of the tenancy. When either decides to terminate that arrangement, in due course, for any new underletting, notice will be given notice.
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. More ramblings atleaseholdpropertymanager.blogspot.com