Vendors staying on as tenants in BTL

Tenancy Types and Management

Hi All, I'll soon be purchasing a flat on a buy-to-let mortgage (as a first-time landlord), and the vendor (who is the current owner/occupier) has asked if they can stay on for a month or two as a tenant because they are waiting to have work done on the property they are buying. My instinct is to say no because it seems like extra hassle e.g. I will need access prior to the start of any tenancy agreement to fulfil my legal obligations as a landlord (arrange gas/elec safety docs, etc), and it's extra cost/hassle to draw up another tenancy agreement so soon after the first one.

But I'd also like to be aware of any legal issues or other risks that allowing them to stay on may raise. My mortgage conditions only state that the tenancy agreement must ensure "vacant possession at the end of the term of the tenancy". Am I missing anything obvious?

Thanks for any advice.