UK Property Law
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Thanks for your question.
If the landlord requires possession at the end of the term of your tenancy agreement then he must have serve a notice under s21 Housing Act stating possession is required. If he has not then you do not need to leave the property until you have received the correct notice.
If the Landlord/agent has not done anything then your AST will automatically turn in to a statutory periodic tenancy and will run on the same terms as your currently tenancy from one rent period until the next. They must still serve the above notice in order to obtain possession (although they will have to make an application to court for an order for possession if you do not leave when the notice expires).
Sounds like the have made a mistake, outline the above to them and they will serve the notice on you. It will have bought you some time though.
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