There can be many requirements before you can apply for a British passport according to the UK Immigration Law. Before a passport can be issued to you, you need several stages of processing including interviews. Getting a passport relatively takes more time unlike the passport renewal; it is an easier process and takes a little waiting time. So it is wise to make travel arrangements after acquiring a passport and allowance at least six to seven weeks time just to be sure there is no hold up. Then applicants who wish to renew their passport or apply for a lost passport replacement should process their documents before the passport expires.
After all your requirements are met in accordance to the UK Immigration Law, the application for British passport is made to the Home Office, or more specifically, the Identity and Passport Service or IPS. If you are abroad and wishes to apply for the same purpose, you may do so in the embassies or consulates in your country. Better yet, before you make your travel arrangements to the destination of your choice you must keep the embassies contact information numbers listed in your diary in case you need a replacement passport.