Letting Agent Fees during periodic tenancy

Letting Agents

I have had the same tenant in my property for the last 10 years and each year I have renewed the AST with the same agent and paid the agreed re-letting fees. For various reasons I have decided not to renew this year and have allowed the tenancy to become a periodic tenancy. The agent says that 'A Periodic tenancy is an extension of the tenancy. Fees are charged on the rental income, not on the actual AST itself'.

The phrase in the AST relating to this is 'The agent will charge the landlord 4% + VAT of the total rental price of the entire term of the renewed or extended tenancy'.

Is the agent entitle to charge a fee now that the tenancy has become periodic?