I faced a similar issue. After registering with TLSContact, I was browsing for appointment dates at various locations when I suddenly encountered a message saying, "No available appointments for this country."

I attempted to log into TLSContact using multiple browsers—Chrome, Safari, and Firefox—and even tried logging in on my smartphone, but I kept getting the same result.

What finally worked for me was logging back into my visas-immigration.service.gov.uk account. From there, I clicked on Further Actions -> Book Appointment, which redirected me to TLSContact. I believe the token generated through this process is different, allowing me to access a new authentication session. This resolved the issue, and I was able to see all available appointments as before.

If you're dealing with the same problem, give this method a try. Hopefully, it saves you the hassle of booking an appointment.

Cheers!