It's been really interesting to hear the side of people with first hand experience of the issue...the media do like to exaggerate for a good story. I also saw the S/Times headline about 1 murder a week by the mentally ill.
I know it is rare, but I was aggressively hounded by an obviously mentally ill guy who was commuting alone from Berks into C.London.
It was the scariest period of my life because I knew this guy was not only aggressive, but clearly not rational. I was terrified of my journey to work because this guy would target me specifically. if he saw me on the platform, he'd storm up to confront me. And it was escalating from aggressive gestures to cornering me in tube carriages and verbally abusing me. His fists were clenched so tight...he could barely contain his anger.
I reported it to the Transport police and felt like a complete idiot until it was clear I wasn't the only woman who had reported this. It got written in a log book, presumably with the other incidents, and that was it.
I changed my travel habits, but that guy continued unsupervised on his daily journeys.
It may be rare, but for 'unconnected' members of the public it is terrifying. And more terrifying was the idea that there was clearly NOONE supervising this guy, and no mechanism to alert his carers about his behaviour.