Tenant Notice Periods and Section 21 Rent Rules

What happens if I serve a Section 21 notice to end an assured shorthold tenancy, but the tenant doesn't give me the full one month's notice before moving out? Am I entitled to charge rent for the full notice period?

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Apportioned Rent

The common law position is that where a tenancy ends midway through a tenancy period, the landlord is entitled to receive the full payment of rent for the entire period.