Another alternative is the online application. My sister has just used this and her new passport came back quickly (I think between a week and two weeks, the old one arriving back first).
You fill in your details online, they then post you a pre-completed form and envelope. You return the fee, your photos and your old passport, and sit back and wait.
Except they have now updated the system, so you pay online at the time you fill in the form using a credit/debit card. Saves having to write a cheque.
Comes down to personal preference at the end of the day - many people prefer the Post Office to have a look over the form before sending it, but you do pay for this of course.
