@Dora31 Sounds like you've already done the 3 things you're supposed to:
1) Ask the guest what time within your scheduled check-in window they plan to arrive.
2) If no response, inform them of when that window will close.
3) Inform them of whatever time, if any, you can accommodate next-day check-in.
On that last point, you're not obliged to admit a guest to the property at any time after the check-in window on the date they're booked to arrive. Your cancellation policy still applies if the guest is a no-show. But since the booking wasn't cancelled before the check-in date, Airbnb still allows you both to review each other (UK law actually requires them to allow this).
It sounds like you're better off not allowing this person into your home, but you might want to start thinking about how you'll publicly respond to a revenge review. You can also adjust your calendar settings to block same-day bookings and/or turn off Instant Book, because neither seems like a good fit to your hosting setup.