Depending on the exact nature of the information and how they have posted it (Have they sent the information to someone else? Have they posted it via their own account? Who has access to the information?), an offence may have been committed.
The offence of harassment may apply. For harassment to be committed, there must be a 'course of conduct' (i.e. two or more related occurrences). The information does not necessarily have to be violent in nature, but must be oppressive and need to have caused some alarm or distress. See Q497 for further information regarding this offence.
If the information is indecent, grossly offensive, obscene or threatening/menacing, then an offence relating to 'malicious communications' may have been committed. This offence does not require more than one incident. You can report any of these offences to your local policing team and they will then investigate and take appropriate action.
If the information posted does not fall under either of the above offences, then you may wish to consider whether the person has committed 'libel' (defamation of character - publishing a false statement that is damaging to a person's reputation). If this is the case, you would need to take action through the civil courts as this would be a civil matter and the police do not have any jurisdiction to assist with this. You should seek legal advice from the Citizens Advice Bureau and/or a solicitor before taking any action regarding this. Please see related information to find your local bureau.
In the first instance, depending on the circumstances and the nature of the information, you may wish to initially make a report to Facebook/Twitter (before contacting the police/Citizens Advice/a solicitor), as these sites have processes in place for such situations, and may be able to simply remove the content and/or close down the person's account.