The Landlord needs to give notice of two months before the end of the fixed term if they do not want the tenancy to continue into a periodic tenancy and would like the tenant to leave the property, since fixed term tenancies automatically become periodic tenancies.
Once the periodic tenancy has commenced, the notice period for either party is the length of the ‘period’, i.e. monthly or weekly, depending on how the rent is paid.
Some landlords may prefer fixed term agreements, rather than periodic tenancies. Therefore, your landlord may suggest renewing your tenancy for another fixed term. You can negotiate with your landlord for the length of time you would like your new fixed term to be if this is the case.