Most landlords will give you a written agreement when you rent property from them, but even if they don’t you still have rights. There are different types of tenancy agreements and the type you have is not determined by your landlord, but by how the property is occupied. The agreement you have with your landlord can give you extra rights but cannot take away any rights that the law gives you. Shelter's online tenancy checker enables you to check what type of tenancy you have and more information about tenants’ rights and responsibilities under that agreement.
The most common tenancy type since 1988 is an Assured Shorthold Tenancy, further details on this type of tenancy are given on the GOV.UK Private renting for tenants: tenancy agreements webpages.