This was during the late 1970s and early 1980s, when the Irish terrorist campaign was in full swing. Everywhere you looked there were signs advising you to report abandoned objects, not to accept packages from strangers, etc. People there were used to it but as a teenager from Southern California I found it both exotic and terrifying.
But that's not how I got my fear of trains. In the summer of 1980, my father and I were waiting for a train in the Tube station near our place. There was a woman next to me, dressed for the office and carrying a purse and a sweater. I turned to my father to ask him something, the train arrived, and I heard screaming. When I looked back there were her shoes, and her purse, and her sweater neatly folded on top, but no woman. She had jumped in front of the train.
I remember getting on the bus to continue our day while the train was shut down. Every time the bus went over a bump I thought it was a body.
Ever since then, I've stood a good long way away from the tracks when I'm in a train station.