It depends on the circumstances. Serious cases fall under the Protection from Harassment Act 1997 which makes harassment an imprisonable offence. If you believe that you are being harassed in a serious way, then you should report it to the police.
False statements could be libellous, but that is a civil matter, and you would have to take legal action. Or, in some circumstances, they could involve perjury, which is a criminal offence.
If the matter is causing you concern, it would be advisable for you to seek personal advice. You could report it to the police, consult a solicitor, or talk to a local office of the Citizens Advice Bureau.