For what it is worth, it took 5 working days for them to renew my passport here, a couple of weeks ago, once I got all the paperwork together. Not sure if re-placing a lost UK passport is more complicated than renewing a passport - I actually had one to show and hand in.
The documentation required here is slightly more onerous than the UK, btw, although if you were born in the UK, there will be the least requirement for information/documentation.
When I checked what constituted 'emergency', for passport renewal purposes, they specifically said business reasons, however pressing, didn't count. They meant things like medical repatriation, life and death situations, etc.