Can they arrest or otherwise apprehend you, or demand to search your belongings? What is their repertoire of capabilities?
TfL Revenue Inspectors can't arrest you - but under certain circumstances they can detain you or use reasonable force to remove you from the 'railway' (which includes TfL buses in London, yes it's weird).
Specifically where you either fail to pay the fare or give your name and address when asked. Section 5 of the Regulation of Railways Act (1889) is the relevant legislation:
(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.
(2) If a passenger having failed either to produce, or if requested to deliver up, a ticket showing that his fare is paid, or to pay his fare, refuses or fails on request by an officer or servant of a railway company, to give his name and address, any officer of the company may detain him until he can be conveniently brought before some justice or otherwise discharged by due course of law.
British Transport Police are another matter entirely - under Section 31 of the Railways and Transport Safety Act (2003) they have all the powers of a constable within their jurisdiction:
(1)A constable of the Police Force shall have all the powers and privileges of a constable—
(c)in a station,
(d)in a light maintenance depot,
(e)on other land used for purposes of or in relation to a railway,
(f)on other land in which a person who provides railway services has a freehold or leasehold interest, and
(g)throughout Great Britain for a purpose connected to a railway or to anything occurring on or in relation to a railway.
(2)A constable of the Police Force may enter property which is or forms part of anything specified in subsection (3)—
(a)without a warrant,
(b)using reasonable force if necessary, and
(c)whether or not an offence has been committed.
(3)Those things are—
(d)a light maintenance depot, and
(e)a railway vehicle.
So if the conditions there are met they essentially are the Police and should be treated as such (they also can have powers outside this jurisdiction in some circumstances)
Under Section 5(2) of the Regulation of Railways Act 1889, revenue officers are empowered to detain you in specific circumstances until you can be brought before the courts or, more normally, handed off to the police for arrest and subsequent prosecution in the normal way.
These specific circumstances are:
- You do not present a valid ticket demonstrating you've paid for your fare;
- You do not provide your name and address when asked;
They do not possess the power to search your belongings. Other powers they (currently) possess include:
- The ability to fine you for not wearing a mask aboard public transport under Section 5 of the Health Protection (Coronavirus, Wearing of Face Coverings on Public Transport) (England) Regulations 2020
- Various powers under the Transport for London Railway Byelaws (made under paragraph 26 of Schedule 11 to the Greater London Authority Act 1999) such as:
- the power to fine you for not wearing a mask within a railway station;
- the power to require you to queue in a given order and follow their reasonable instructions;
- the power to confiscate "potentially dangerous" items from you, such as a loaded weapon, a flammable, explosive, or corrosive substance, or "any item which is or may become dangerous";
- the power to require you to leave the railway or prevent you from entering or remaining on the railway if they believe you are "unfit" through drink or drugs or are carrying any open containers of alcohol with you;
- the power to remove any open containers of alcohol you are carrying;
- the power to prevent you from entering or remaining on the railway if, in their reasonable opinion, you are in an "unfit or improper condition" or your clothing may soil or damage any part of the railway or the property or clothing of anyone on the railway;
- the power to require you to follow their instructions in the event of an emergency in which they feel the interests of safety require it;
- the power to fine you for using a baby carriage or wheelchair contrary to instructions they've issued;
- the power to refuse entry or carriage to any animal which, in their reasonable opinion, may threaten, annoy, soil, or damage any person or property on the railway;
- the power to remove any animal that does any of the above;
- the power to use reasonable force to remove you from the railway if they reasonably believe you've breached any of the Byelaws and are desisting from doing so or refusing to leave once asked;
Any such breach of the Byelaws would be a criminal offence and each offence would result in a fine, not exceeding level 3 on the standard scale, to be issued.
"Railway" in the above list means "trains, track and stations that are part of Transport for London‟s railway, including the London Underground, London Overground and Docklands Light Railway networks".