2 year tenancy

Tenancy Types and Management

Hi all I normally find my tenants and manage all my tenancies on a 6 month AST basis, I have however been trying to sell my own home and the letting side of the agency selling my house has asked for a one off viewing for one of their clients looking to rent a property like mine. The people want to rent my house but have asked for 2 years, I agreed with a break clause for each side but they have come back and said they only want to rent without a break clause. I have said as long as the property is looked after and rent paid etc they can stay as long as they like after the initial AST period expires on a month to month basis but this does not seem to meet their requirements.
As I have lived in the property for 12 years am I right in saying that whatever tenancy is granted I can get possession at any point during the tenancy for me or any member of my family to return to the property, if so this makes their 2 years relatively easy to get out of if they are not taking care of the property or failing to pay the rent?