For people living in London having nationality of UK, you can apply online via an official website for the renewal of your passport click here
a) Completing the application online
b) Get the form, from a post office if situated some where near your residence.
c) If you cant get to the post office, than you can always request the form online which will take 5 days to be delivered to your door step.
d) You can always contact the help line of passport offices in order to Order form by Post.
Find the branch of post office that is located near to you by branch finder, and send the complete application there via post.
You have to send 2 recent passport size photographs. The cost of renewal of British passport is £77.50. However, if you wish for an urgent renewal, the cost will be different.
For more help regarding the filling of the passport renewal form kindly go through this tutorial guide for filling passport renewal form.
For citizens other than British, if the passport was issued to you within last 15 years than you need to contact the relevant embassy; the embassy of your country in UK, along with the following documents:
a) NIC and copy of your previous visa.
b) Renewal fees which varies from country to country.
d) Evidence of your previous (expired of full) passport and you visa of UK.
After you have submitted the renewal application, you will be scheduled an appointment and will be interviewed shortly, where you will b undergoing the following processes: fingerprint scanning, photo shot and verification of documents.
Your passport will be ready to be collected within a period of 3-7 days (for most of the Consulates), urgent cases will take about 2 or 3 days only.