Section 21 Notices Are Invalid When the Landlord Breaches the Tenant Fees Ban

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If you have breached the new rules on tenant fees, then you won’t be able to evict your tenants using Section 21. The Tenant Fees Act 2019 restricted the fees which landlords and tenants may charge to tenants, introduced a cap on tenancy deposits and regulated the operation of ‘holding deposits’. The Act currently applies…

The article is understood and agreed.
As my tenancy agreement was agreed and signed before the date of implementation of this aspect of law, a partial refund was not necessary.
However, after the legal deadline I issued a Sect 21 and then cancelled it a week later in writing and I did not produce a new agreement as the existing one states it will turn into a rolling monthly contract, and I emphasised this in my cancellation notice. The tenant has continued to live in the property and pay the rent as per that agreement, but did not formally accept the cancellation - it was accepted by default as far as I can tell in law.
The tenant now claims that a partial refund is due as I had issued the Sect 21 notice. I disagree on the basis that a new agreement was not produced and the existing agreement catered for continuation beyond the fixed term and the tenant continued to live in my property.
I am due to reoccupy the property as my home at any time, and this was made clear at the outset, and the agreement was written to allow for this.
Has the tenant any grounds for believing a partial refund is due?
Does the issue and cancellation of the Section 21 Notice affect the agreement I put in place, e.g should I have produced a new agreement? I need it to be on a rolling basis for my imminent return!
Views, particularly legal, would be appreciated.