Libel (which is the term applied to 'published' defamatory statements, rather than slander) is a civil offence, not a criminal one, so the police wouldn't get involved purely because of the defamation.
My post here is relevant to that civil offence:
http://www.theanswerbank.co.uk/Law/Civil/Quest ion782024.html
However this is also relevant. Quote:
"(1) A person must not pursue a course of conduct�
(a) which amounts to harassment of another, and
(b) which he knows or ought to know amounts to harassment of the other"
Section 1, Protection from Harassment Act 1997
It's far easier to take a civil action for harassment than it is for libel. A successful action can lead to an order to pay damages for (among other things) anxiety caused by the harassment. It can also lead to an injunction against the offender, preventing further harassment. (Breaching the injunction could lead to up to 5 years imprisonment).
I doubt that you'd be able to get the police interested in pursuing a criminal enquiry but it's just possible that they might consider that the provisions of the Malicious Communications Act 1988 are relevant. (If a criminal offence has been committed it can result in a fine of up to �5000 and/or 6 months imprisonment):
http://tinyurl.com/37tapz
Chris