An applicant just turning 16, who has previously held their own passport, is not required to attend an interview. The passport application should be completed as a 'renewal'.
If the applicant has previously been named on a parent's or grandparent's passport, they are now applying for their own passport for the first time, and must apply for a first passport.
Further reference:
24-hour Passport Adviceline: 0300 222 0000 (see terms and conditions). Calls made to 0300 numbers from landlines and mobile phones are charged to customers at their network provider's national rate. Live operators are available to assist with your enquiry 24 hours a day.