It is in the news that a Metropolitan Police officer is being investigated after a mother was wrongfully arrested for bus fare evasion. However it is not clear, to me at least, exactly what the legal situation was regarding her detention.
Police were at the scene to support Transport for London (TfL) ticket inspectors as part of a "pre-planned operation" to tackle fare dodging.
The Metropolitan Police later said that the woman did have a valid ticket and acknowledged the incident had been distressing for her and her child.
They also said the woman "did not" provide her ticket as she got off the bus and when spoken to by a TfL inspector, a police community support officer (PCSO) and lastly by a police officer "she continued to walk away and did not provide her ticket for inspection".
It is not clear what '"did not" provide her ticket as she got off the bus' means, but for this question interpret it as "She was within the bus when the ticket inspector started talking and outside of the bus and had taken a handful of steps by the time they finished talking and she had an opportunity to respond".
If we concern ourselves only with the initial encounter between the woman and the TfL Revenue Inspector from this answer their powers are defined by the Regulation of Railways Act (1889) which state:
(1) Every passenger by a railway shall, on request by an officer or servant of a railway company, either produce, and if so requested deliver up, a ticket showing that his fare is paid, or pay his fare from the place whence he started, or give the officer or servant his name and address; and in case of default shall be liable on summary conviction to a fine not exceeding level 2 on the standard scale.
The answer also says "the 'railway' (which includes TfL buses in London, yes it's weird)". I guess the question is are you "by a railway" while standing next to a bus you have just alighted from? What about once it has driven off? What if you have walked a few steps? Is that the same as "do you need to show a TfL Revenue Inspector your ticket" in the same situations?