Well let me tell you what a total mess the passport service is in. I booked a 7 day fast track on the 31st March, appointment on the 9th April, flying on the 18th April, passport is still not here. In fact when im able to speak to them without 3 hour waits or the call being cut off they have told me its not even been printed and they have no idea why.
Good luck but iv just lost 4.5k cause of the useless uk passport service