My British passport expires early next year, so I decided to renew it while I was back in the UK for a few months. I applied on-line, paid £82.50 for the standard service, and sent my old passport to an address in Corby, on 23 May. I received an e-mail advising me at each stage of the process, and received my new passport, and my old passport back, this morning, 6 June. That is a fortnight, only 14 days, from when I applied! I am quite impressed.
TLDR : Answer Summary
A British expat shares their positive experience renewing their passport online, receiving it back in just 14 days. Many commenters discuss their own passport processing times, noting variations in speed between the UK and other countries, such as Thailand.