here is the first lines from the direct.gov.uk website headed ''Urgent passport applications'' ;-To get your passport within two weeks, you will need to apply in person at one of IPSs Regional Passport Offices. You can use:
* the Fast Track one-week service
* the Premium one-day service
here is the text 6 lines later ;- Making appointments to visit in person
Demand for appointments in all IPS regions is usually very high. You should therefore allow up to two weeks for your appointment date. You cannot book appointments more than two weeks in advance.
here is the link to the site ;- http://www.direct.gov.uk/en/TravelAndTransport/Passports/howlongittakesandurgentappplications/DG_174149
So there we are typical government double talk
To sum up - If you need your passport within two weeks you may have to wait two weeks for the appointment to apply.