The plan is that
all first time applicants for an 'adult' (16 years and over) passport will have to attend an interview. Since 1 June 2007 the Identity & Passport Service have been gradually increasing the percentage of applicant who're called for interview; by now it's likely that most (or possibly all) applicants will be required to attend.
I&PS recommend allowing at least 6 weeks between applying for your passport and your intended travel date. The first part of the process is routine ID checks (such as the electoral roll). When these have been completed, you'll be invited to book an interview. Your passport should be issued shortly afterwards. Given that you're already 2 weeks into the 6 weeks that I&PS aim to issue a passport within, it's likely that you should hear from them soon with regard to any interview.
The interview takes about 30 minutes. You can choose which of these locations to attend:
http://www.ips.gov.uk/passport/find-interview- office.asp
Source:
http://www.ips.gov.uk/passport/interviews.asp
Chris