Fixed term tenancy
In most cases a tenancy will have been granted by a landlord to a tenant for some fixed term. Sometimes this is known as a term certain or initial period but the Housing Act 1988 refers to it as being a fixed term tenancy.
It used to be the case under section 20 Housing Act 1988 that the fixed term had to be for a minimum period of 6 months and a special prescribed notice be given before any tenancy was granted but this rule was removed for all tenancies granted on or after 28 February 1997.  Since 1997, a fixed term can be granted for any period a landlord and tenant wishes to agree. In fact, no fixed term needs to be provided whatsoever and a periodic tenancy could be granted from the outset.
There is a small spanner in the works though. Under the Housing Act, if possession is sought, a judge cannot make an order for possession to take effect sooner than 6 months from the first day the tenant moved in. Renewals are ignored for this calculation. Notwithstanding this, possession proceedings can be commenced before 6 months (assuming the fixed term was for less than 6 months) and it’s only the date in a possession order which is affected by this rule.
Last day of fixed term
There is no implied right that a tenant may leave at anytime during the fixed term. However, the common law is that a fixed term ends on the last day. Therefore, in many cases it will likely be the case that a tenant can leave within the 24 hour period that is the last day. The Office of Fair Trading state that it is not possible to seek notice from a tenant prior to the last day but we’re not sure that is entirely correct but has not been tested. 
Where a tenant is in occupation the stroke of midnight following the last day, a periodic tenancy will start. What type of periodic tenancy will depend on the terms of the tenancy agreement.
If there are joint tenants, all the tenants would have to leave on the last day otherwise a periodic tenancy will arise. Also, if a notice to quit is given by the tenants expiring on the last day of the term, the notice will have to be from all the tenants. 
Statutory periodic tenancy
If the tenancy agreement remains silent on what happens after the fixed term ends and the tenant remains in occupation, a statutory periodic tenancy will arise [section 5 Housing Act 1988]. Similarly if a landlord enforces a break clause during the fixed term, a statutory periodic tenancy would arise.
A statutory periodic tenancy is effectively a brand new tenancy granted by the same landlord to the same tenants under the fixed term tenancy.  The terms of the new statutory periodic tenancy are the same as those that were contained in the fixed term tenancy (except those relating to rent increases during a statutory periodic tenancy it would seem ). The periods of the statutory periodic tenancy are the same as the last rent which was payable under the fixed term tenancy.
For example, if the last rent that was payable under a fixed term tenancy was a calendar month from 15th January 2014 to 14th February 2014, the periods of the statutory periodic tenancy would be calendar monthly from 15th of a month to 14th of the next month. This periodic tenancy would ‘roll on’ forever until either party gives notice and if necessary obtains a court order.
Before changes made by the Deregulation Act 2015, it was advised to re-issue prescribed information within 30 days of the new statutory periodic tenancy arising but this is no longer necessary in most cases (see deposit heading below).
No statutory periodic tenancy will arise if the tenant is granted another tenancy for the same dwelling-house which takes effect immediately at the end of the fixed term tenancy. This is often referred to as a ‘renewal’.
If a renewal is given sometime after the statutory periodic tenancy has arisen, the periodic tenancy will end and the new tenancy will start from its commencement date. This means the tenant is in a state of continuous protection by either statute or contract entitling the tenant to remain in occupation.
Contractual periodic tenancy
As discussed earlier, instead of a fixed term tenancy, it is possible to grant an assured shorthold tenancy with no fixed term. This would be a contractual periodic tenancy from the outset and would ‘roll on’ following the rental periods.
In addition, it’s possible for a fixed term tenancy to ‘continue’ as a contractual periodic tenancy at the end of the fixed term. The resulting periodic tenancy which continues would in essence be the same as a statutory periodic tenancy in that it would ‘roll on’ for the same periods as the rental periods although this could be changed in the tenancy.
Most landlords would not notice the difference between a statuary or contractual periodic tenancy but legally there are important differences and on balance a contractual periodic tenancy will favour the landlord.
A statutory periodic tenancy only arises if a fixed term tenancy ‘ends’. If the tenancy ‘continues’, it never ‘ends’ and so the problems that have arisen since Superstrike do not apply although these have in the main part been fixed by the Deregulation Act 2015.
That being said, there are still advantages for council tax purposes should a tenant abandon a property during a periodic term. Depending on the local authority policy for council tax, where the tenancy was a statutory periodic tenancy, the landlord would be liable for council tax even when there is a periodic tenancy continuing and the tenant is not in occupation. However, where the continuation was a contractual periodic tenancy and the fixed term tenancy never ended, the tenant may well remain liable for council tax where insufficient notice has been given including possible abandonment.
One downside to a contractual periodic tenancy is that in the recent Spencer case, it was held that a section 21 notice served during a ‘statutory periodic tenancy’ did not have to expire on any particular date (previously it was thought such a notice must expire on the last day of a period). It would seem Spencer does not apply to a contractual periodic tenancy though because the fixed term tenancy never ends. This doesn’t really matter though because a section 21 can be still be served – it’s just that it must expire after the correct date which our notices make easy by not having to insert a calendar date. Further, the Deregulation Act 2015 will introduce soon (likely October 2015) the removal of the requirement to expire the notice on any particular date for all types of tenancy.
If a tenant wishes to leave during a periodic tenancy, they must give notice. The notice will need to be at least 4 weeks to a calendar month depending on the rental period and when served during a periodic tenancy, notice from one of several tenants is sufficient to end the tenancy for them all.
Fixed term renewal
At any time, the landlord and tenant(s) can agree a new tenancy. Often this is done at the end of the fixed term for another similar fixed term to the previous (for example 6 months) and is referred to as a ‘renewal’. If a fixed term is granted whilst there is already another in place for example if a new tenant is to be added, the old tenancy is automatically surrendered and the new one takes effect.