Withdrawal of application timescale

Hi everyone, My current passport application is stuck on the documents received since 15th March. I need to go abroad in an emergency due to a family member falling ill. The only option I have realistically is to withdraw application and do fast track application. I wanted to know when I send my withdrawal of application letter how long does it actually take for my passport to come back? I'm reading many users on here sending their documents but its not updated as received for weeks. When I called they mentioned it takes 11 working days but forgot to ask, but i'm going to assume that will be after they have received the letter / checked it. So generally how long does this initial process take? I'll have to send the application to the Durham office. Any advice will be appreciated Thanks