I'm sorry to hear both the police & your manager were hopeless in their response. It's not good enough.
I do think that your colleague is in the realms of criminal harassment - 'where a person pursues a course of action which amounts to harassment of another individual, and that they know or ought to know amounts to harassment. Under this act the definition of harassment is behaviour which causes alarm or distress.'
The fact he has been previously spoken to by management about his behaviour shows that he knew his conduct was causing distress and was unwanted. He has gone one step further and escalated his behaviour.
I get the point that at the moment what you have is based on hearsay - but that is exactly what the purpose of an investigation is to do - to gather evidence. That is the case whether it is a criminal or a disciplinary investigation.
I know in our police area, where there is an allegation of harassment, but police do not believe the offence is complete (usually because there isn't evidence of a course of conduct, or knowledge on the part of the perpetrator that the conduct was unwanted), police issue what is known as Police Information Notices - basically it is a warning that if the person continues the alleged conduct, they will be arrested for harassment.
I would go back to the police and advise them you wish to make a report of harassment and ask for a crime number. If they refuse to take any action, then you can consider a complaint against the police.
In terms of your employer, get a copy of your grievance or bullying & harassment procedure. Follow the procedure to the letter and submit a grievance / B&H report. Don't be fobbed off by your manager - if needed, go above her head to her manager & HR.
By his actions, this man is effectively trying to make it impossible to work there. By their lack of actions, your employer is enabling him.
Do you have any legal cover on your house insurance? It might be worth looking into whether you could get legal advice on it. A legal letter may also focus the minds of your employer and make them realise how their lack of action could leave them really vulnerable to a claim of constructive dismissal.
One thing to be aware of - I have seen it time and time again - people will very often tell you about so and so who left because of the same thing, or that he did it to someone else. When it comes to putting pen to paper though, people suddenly don't want to get involved. I would echo pp advice about not conducting your own enquiries.
I also know you have said on the thread that you won't be contacting his wife, but please, please, please, could other posters stop suggesting this? It will leave the OP wide open to counter allegations and will serve no purpose. It's really bad advice.