If you receive two or more nuisance or threatening communications this could amount to an offence of harassment. For harassment to be committed, there must be a 'course of conduct' i.e. two or more related occurrences. The communication does not necessarily have to be violent in nature, but it would need to be oppressive and cause alarm or distress.
The incidents must be related and must not be two isolated incidents. The further apart the incidents are, the less likely there is to be an offence of harassment. However, all the circumstances of the incident will be taken into account when determining if an offence has been committed.
The law takes into account the "reasonable person" test. This means that if it was felt that a person of reasonable firmness i.e. the average person on the street would not be alarmed or distressed, the offence is not committed. The offender must also be aware that the course of conduct they are pursuing would cause the victim to alarmed or distressed.
A and B were partners, A finishes the relationship but B is not happy. B sends 30 communications over the course of a week begging A to reconsider. If A is then distressed by this course of action, an offence of harassment is likely to have been committed. Note however, if A was not distressed and ignored the communications, then no offence of harassment would have occurred.
There are two possible ways of dealing with this type of harassment; through the police or the civil courts. To commence civil proceedings you should contact the Citizens Advice, please see the link in related information to find your nearest one. Alternatively, if you would like police involvement you can contact your local policing team via the non-emergency 101 number.