2 issues with your statement...
1) either your lease has continued under the provisions of the Landlord and Tenant Act 1954 - your obligations remain and you're required to give 3 months notice if you intend to vacate.
2) If your lease was contracted outside the Landlord and Tenant Act 1954 then you're trespassing.
In any event. Deposit should have been accounted for at completion, lease and deposit deed should make reference to landlord and successors in title. No need necessarily to need a new rent deposit deed. What does the lease specifically state in relation to this requirement for a new rent deposit deed?
The opinions I give are simply my opinions and interpretations of what I have learnt, in numerous years as a property professional, I would not rely upon them without consulting with a paid advisor and providing them with all the salient facts BSc (Hons)