The law has no objections to girls under 16 having an abortion.
However, it will require the consent of two doctors, who in normal practice would like to discuss the abortion with the girl's parents.
I imagine something like this would be impossible to keep from anything but the most dysfunctional parents anyway, so why not be open and honest from the outset....
http://www.adviceguide.org.uk/index/family_parent/health/young_people_health_and_personal.htm