Download the application form from the British government website. Complete sections 1, 2, 3, 4, 5 and 9 of the form, and also section 6 if the application relates to a child ages 12 to 15. Be sure to mark the box on the first page stating you wish to replace your damaged passport. You must ask a counter-signatory to complete section 10; she should be a British, Irish or European Union passport holder who is in a professional occupation, such as a police officer or teacher, and has known you for at least two years.
Your application must be accompanied by two passport-style photographs. British criteria differ markedly from those used in the United States, so be sure your photographs conform. They must measure 35 mm-by-45 mm (1.4-by-1.8-inches), be in color and have been professionally printed. You should be shown looking directly at the camera with a neutral expression on your face. Ask your counter-signatory to certify the back of one of the photos by writing “I certify that this is a true likeness of (your name),” then signing it. In addition, you have to send your current damaged passport with the application.
As of September 2013, replacing a standard adult passport costs 128 pounds, plus an additional 9.70 pounds to cover the cost of returning your new passport by courier. Pay in pounds sterling with a credit or debit card by completing the “Paying by credit card or debit card” form, downloadable from the British government website. Be sure to complete all the sections, and place the form in an envelope with the rest of your application.
Mail the application and all the supporting documents, including the payment form, to Her Majesty's Passport Office, OVS-D, Millburngate House, Millburngate, Durham, DH97 1PA, United Kingdom. For the security of your application, the British Passport Office recommends using a courier.