The extent to which slippery rails can cause trains to be unable to stop?

I don't think the Shepperton incident has been mentioned yet, so by way of light(er) relief - see the Wiki entry:

Accidents and incidents[edit]​

On the 21st of April 1982, a British Railways Class 508 train running the 06:34 service from London Waterloo to Shepperton crashed, demolishing barriers and a wall. The train also slid into some new pedestrian crossing lights, rendering them unusable.[3] The crash was initially believed to be the result of braking tests the previous night, which involved applying grease to the tracks, and that the grease may not have been sufficiently cleaned off, however it was later found that the train's brakes were faulty.[4]