It is not an offence to beg on the street. Though if a beggar was to behave in a manner that caused the public alarm, e.g. shouting or acting in an intimidating manner, then they may be committing a breach of the peace.
It is however, an offence for a person to cause or procure a child under 16 years of age to beg. If you are concerned or alarmed by the behaviour of a beggar then you should inform the police who will then investigate.