Is it a crime to allow my 16 year old son to leave home and move in with his girlfriend aged 19? He's not happy at home and doesn't get on with his step father, he was always spoilt and is a only child.

Where? Even if he leaves you are LEGALLY responsible for him until he reaches legal age.

You can give guardianship to the girlfriend's parents OR you can ask the Court to emancipate him to get out from under any legal responsibility.