You have no legal right to the information that you are asking for. In that respect, the tenant is quite correct. However, even if you were shown a birth certificate, there is no guarantee that the birth certificate is the birth certificate of that person.
I must admit, I have never had a landlord (over 25 years in the legal profession) ask for the proof of date of birth of the tenants guest.
I’m afraid that if you carry on with this is likely that you could end up on the receiving end of a claim for compensation or an injunction (or police attention!) for either harassment or breach of covenant for quiet enjoyment.
You could serve a section 8 notice for breach of tenancy agreement which the tenant would have to oppose and a judge would decide whether he has breached the terms of the agreement or not.
You could serve a section 21 notice because the tenancy has now become periodic and end the tenancy in two months.
I appreciate that you probably don’t want to lose the tenant but you don’t want any subletting either but there is no magic solution to compel the tenant to give you the identity of whoever is staying there.
I’m sorry, I know it’s not the answer you wanted.
Can I clarify anything else for you?
I’m happy to answer any specific points arising from this.
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