Suicide is not an offence in itself. The offence was abolished by the Suicide Act 1961. (Section 1 simply reads: "The rule of law whereby it is a crime for a person to commit suicide is hereby abrogated.").
However, aiding, abetting, counselling or procuring someone else's suicide or attempted suicide is guilty of an offence punishable by up to 14 years imprisonment. The offence requires the consent of the Director of Public Prosecutions to prosecute.
Suicide was a crime because it was not believed that a person's life was their own for these purposes – the origin of the prohibition is religious. When that belief ceased to be as widely accepted the law was changed.
Suicide is however a form of antisocial behaviour, which is sick.
[EDIT: Slow today…]