Periodic Tenancy

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Does a AST automatically become a Periodic Tenancy after the fixed term? I ask this because Hammersmith and Fulham Council are attempting to charge me for the period after a fixed term had finished, up until a new fixed term agreement was signed. The flat was tenanted and as far as I'm concerned a periodic tenancy was in place after the fixed term finished and up until the new fixed term agreement. I have quoted Section 5, clause 2 and 3 , of the Housing Act to them. Is there anything else I can do. Where do I stand? Thanks.