If the tenant is occupying the property under an assured shorthold tenancy which expires then the tenancy will become a statutory periodic tenancy, this means that the tenancy continues on the same terms but from one rent period until the next (eg. month to month if paid monthly).
If you wish to take possession in these circumstances then you would have to serve a 21 Housing Act 1988 notice giving him two months notice with such notice to expire on the last day of a rent. It is very important that the notice is in the correct form and a simple google search for "s21 notice statutory periodic tenancy will generate a list of document providers.
If the tenant does not leave by the expiry date on the notice then you will need to apply to the court for a possession order. Provided the correct procedure has been followed in issuing the Section 21 notice, the court will have no choice but to grant the possession order so that the tenant vacates. If he does not after such an order you can apply for warrant for execution from the Court so that the bailiffs evict him.
If he has persistently paid rent late then you could serve a s8 Ground 11 HOusing Act 1988 for which the notice period is only two weeks and you could do this now. If the tenant does not leave after the notice period and the Court accepts that they have persistently paid rent late then they will make an order for possession.
If you sign a new tenancy agreement with the tenant then they will have a right to possession of the property during the term of that tenancy agreement.
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