Provided you have protected the deposit, then you need to obtain and complete form N5A from your local county court to apply for a possession order via the "accelerated" procedure. A fee of £150 is also required and the form should not be submitted until your tenants fail to move out on the 5th. The judge will now consider your application in chambers: if your tenants do not lodge an objection, and you have got the paperwork right, a possession order will be granted. This then enables you to use court bailiffs to evict the tenants. If the tenants do object then (hopefully) the judge cannot extend their tenancy by much before they will be required to leave. You need to take out another action in the small claims court to regain your rent as it is due from these tenants until the day they actually move out.
Any information given in this post is based on my personal experience as a landlord, what I have learned from this and other boards and elsewhere. It is not to be relied on. Definitive advice is only available from a Solicitor or other appropriately qualified person.