Mari-Simon Cronje died while celebrating a friend's birthday in September 2010 after she fell from the banana boat. She died from severe leg injuries after falling into a lake at the Prince's Sporting Club in Bedfont in west London.
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"All it takes is for somebody to see me - and I could just die, just like that. I could want to go to the shop and not come home."
Before the killing, Peters searched the internet for "serial killers", "treatment of child killers in prison" and "premeditated murder".
Arriva Rail North, Greater Anglia and South Western Railway are all affected.