Just because you do not have a written agreement, does not mean you do not have a tenancy agreement. Once an individual has moved into a property and has started paying rent for a term, a tenancy is created. This means that even without a written tenancy agreement, a tenant is still covered by the Protection From Eviction Act 1971.
If there is no tenancy agreement, a tenant cannot be given a section 21 notice for eviction. Instead, a landlord must use a section 8 notice (with a ground for eviction). To be able to evict a tenant in the absence of a written tenancy agreement, a landlord will need to apply to the courts for a possession order.