From the CAA's website:
Same day services’ conditions
The following conditions apply:
•You or your representative must arrive before 11:30am with all relevant documentation completed otherwise your application will have to be re-submitted.
•Applications are processed on a 'first come, first served' basis.
Multiple applications
•If you are applying for more than one applicant, the airline or organisation must request this in writing at least one working day in advance by emailing
[email protected].
•Requests for multiple applicants will be accepted subject to business demands.
We are unable to provide a same day service for application for licence issue or upgrades, or any other service not listed above; however the applications may be handed in at the Public Counter and will be subject to the 10 working days turnaround service.
So you could peddle your way round the M25/M23 and deliver the docs in person. They MIGHT look through your application to see if it's all in order. Probably better than the uncertainties of the post.
TOO