Hello Alastair,
there's no specific article in T&C that regulate this topic, and many Host simply put in their rules that unregistered guests are not accepted, however:
Art. 8.1.2 states:
Upon receipt of a booking confirmation from Airbnb, a legally binding agreement is formed between you and your Host[...]
By "you" we refer to the guest. What is saying the binding agreement? 1 person? 7 person? Those pointed in the binding agreement are the ones who can enter in your house, the only problem is that if you do not have the names, as usually only AirBnB have them, they may "exchange" themselves in order to get in the house but still remaining in the limit.
Furthermore, Art. 8.1.3 says:
If you book a Host Service on behalf of additional guests, you are required to ensure that every additional guest meets any requirements set by the Host, and is made aware of and agrees to these Terms and any terms and conditions, rules and restrictions set by the Host.[...]
If the primary guest do not respect the booking contract (art. 8.1.2.) or his guests fail to comply with the rules, it's a breach in the contract and you can enforce it and cancel calling AirBnB.
As the event it's already happened, the only thing you can do beside a review and a report (if you find the write option that may describe the situation), it's simply prepare yourself for the next time.
From a personal point of view, instead, from your words I can desume that you have a house specifically set up to work as a business, so or you put a concierge or this will continue to happen, after all it's also happens with hotels, when people get in and at the reception the employee is missing because maybe is in the toilette who knows, and the regular guest sneak inside with a friend.
