If they won’t hold the train then there should be a standard procedure for dealing with the consequences.
A machine that will read your ticket and print you a chit saying your train was called late, you were there, and giving permission for alternative options, which should include getting the next train at no extra cost, a free seat reservation if you had one before, etc etc. And preferably some kind of freebie like a free drink while you wait
The railway has let you down, they should look after you, and it should be as stress free as possible (hence an official piece of paper rather than worrying about whether you understood correctly or might get a fine)