Never seen so many questions in a post.
"The evidence of PC Thain at the Nichols inquest was that he "was not allowed to leave his beat unless he was called".
Can any of the police experts on the board tell me what this actually means? "
Just as you state, a constable was not permitted to leave his beat unless the circumstances warranted it, either an emergency or he was ordered to.
If such an emergency occurs off his beat, he would tend to the situation, calling constables from nearby or the nearest station, for aid, usually by sending members of the public as runners or using their lamp. The use of a whistle was the last option, as it often drew crowds which would need controlling.
Once reserve constables have arrived, and the situation managed by a senior officer, the beat constable would return to his beat, and continue until his shift ends.
There was no need for anyone to lie when it came to protocol. The likely reason why Mizen did lie may be due to the fact he seems to have completed his knocking up prior to inspecting the Bucks Row scene, and besides, he probably felt that it was J divisions issue, rather than his H divisions.
PS All of this is in my new book....plug, plug, plug.