I want to say that he has the option to request permission to appeal to the Supreme (?) court if he loses this appeal, which would be the final end game. But no guarantee that they would accept the appeal (I think, definitely not an expert in this)
You are correct, @ellesar! Harry gets two bites at the cherry to get permission to appeal to the Supreme Court if he loses. First, he applies directly to the Court of Appeal - the same judges who will have just determined against him. If they says no, he can then apply again, directly to the Supreme Court. If they say no, he is out fo options.
Obviously if the Home Office loses today, they would have the same ability to apply for permission to appeal.
The Supreme Court only hears appeals of matters of law that are in the public interest. So it’s not immediately obvious that they would take an appeal brought by an individual in relation to the decisions of a body which has a very limited scope.