How would an inspection prove whether you were working from the flat or how many people were visiting you? Assuming you don't have work stuff lying around everywhere when your landlord comes round, obviously.

An inspection is normally to check the flat is OK and you haven't damaged anything, not to monitor what you're doing there. I would arrange the inspection and just say you have no idea what they mean; ask why you are being spied on and what the number of friends and family you have is any of your neighbours business? Do you all have the same landlord?

Do you do a lot of short bookings in the evenings when people are in, or are we just talking about a couple a day? Have you been at your flat for long and when does your tenancy finish? I'd be panicking too I know, but at this point they might just be fishing