UK/ANZAC and Japanese air units may fly over each other’s territories (outside of China) when they’re not at war. The rules at the top of page 8 that apply to neutral territories apply only to neutral territories, such as the Mongolian territories. Neutral powers have different rules, as outlined in the political rules.
Technically, Japan, China and UK/ANZAC are not neutral anyway, as they are each at war with someone (Japan and China are at war with each other, and UK/ANZAC is at war with Germany). Only the US is truly neutral, as it is at war with no one. That’s why its rules are even more restrictive than other powers’ rules. While the US remains at peace, its air units may not fly over other powers’ territories, and vice versa.