I worked with the BTP on London Underground in the early nineties. The bread and butter were security alerts, assaults, drunks & pickpockets, criminal damage, trespass, theft, robbery and fare evasion.
One of the worst jobs on the underground was dealing with the suicides or one-unders as they were commonly called, my overriding recollection of these was the impatience of other passengers who simply didn't care that someone was dead or fatally injured.
It has to be remembered that a lot of railway property is considered private property and offences were covered by a huge number of byelaws which cannot be dealt with by criminal law or regular police. Specialist knowledge is required when working in a railway environment especially on electrified lines. All BTP officers train with the Met or County forces and receive the same training and have the same powers of arrest. They just get to ride trains as a bonus.