Tenancies usually start with an agreed fixed-term, (for example 6 or 12 months) during which time both parties are contractually bound - the tenant to pay rent for the full term, and the landlord to allow their exclusive possession and quiet enjoyment.
Once the fixed-term of a tenancy has expired, however, unless a new fixed-term is agreed to, all tenancies automatically become periodic tenancies. These are based on the rent payment period - weekly or monthly etc. The periodic tenancy can then continue on until one side, landlord or tenant, gives notice.
At the end of the fixed-term, therefore, there is no legal requirement for either party to do anything - the tenancy can continue on indefinitely on a periodic basis and on exactly the same terms as the original agreement, which still fully applies.
When the fixed term of an Assured or Assured Shorthold Tenancy comes to an end but the Tenant stays, a periodic tenancy automatically follows the fixed-term if the parties do nothing (i.e. they do not sign another agreement) and the tenancy will be on the same basis as the original agreement, with all the same clauses and conditions being operative.
The period of the tenancy will depend upon the rent payment schedule: if the rent was paid monthly under the original fixed term, this will become a monthly periodic tenancy, or a weekly periodic tenancy if this was the payment schedule. In the case of a periodic tenancy.