I’m really sorry but I don’t know for definite. I have picked up a little knowledge just from reading threads on here. A recent story was someone turned up without an appointment at their local passport office and had a passport by the afternoon – but I think they already had an application sitting idle at another office (not cancelled like yours).
Perhaps you would need to book a premium 1 day or fast track 1 week appointment – @ukpassportcheck on twitter is a good place to keep an eye on for guidance on getting an appointment.
Sorry I can’t be of more help.