If your British passport is lost of stolen then you need to fill in an online application form-and their is no fee to do so, once you report it online then you have to obtain a form from the Post office to apply for the replacement passport please be advised that it has to be replacement of the passport neither the renewal.

How Long will it take to obtain the passport:

Postal service will take upto 3 weeks and it will cost you £72.50, however you can apply on same day as well.

You need the photo to be counter signed by a person who must have a professional standing (Solicitors, Barrister, GP bank Manager) and hold British Passport.