As you are not stranded abroad having lost or had your passport stolen then you can not get an emergency passport. However you can have a faster application. There is premium service (£128) which you can get a passport 4 hours from when the application is accepted or the fast track service (£103) which will deliver the passport to you within a week of the accepted application.
You will need to book an appointment at the passport application centre to get the application accepted. This can take up to 2 weeks. The location of the centres are in London, Liverpool, Peterborough, Glasgow and Newport, and Belfast and Durham.
You must bring a completed application form and supporting documents to your appointment. Get a passport application form and guide on how to fill it in from a Post Office.