Hello.
From the tone of your message, it implies your passport isn’t actually lost but you just want it processing quicker.
I was and am in a very similar situation. I sent my passport and it took 4 working days before it was added to my application. From looking on this site though this can take a few weeks, and a post on the passport office twitter says it can be 2 weeks.
I submitted my passport renewal by the normal channels a few weeks ago as I expected a prebooked trip to the Balearics was not going to happen. Roll forward a few days and the trip was back on.
My research provided the following info:
It is possible to withdraw a passport application and they will return your existing document to you (you lose your initial application money).
This has to be done via writing so in theory could take the same length of time for that to be received, processed and your old docs returned.
It is not possible to do the 1-day passport application without your old documents.
It could be possible to withdraw your application, then say the old one is lost and do the 1-week fast track (i considered this too).
HMPO will not provide any info as to where you are in the queue or how long your application is going to take. All they will say is it can take up to 10 weeks.
My strong advice here to anyone reading this is to use either the 1-week or 1-day service if you need the passport in a hurry. The extra £100 is well worth the peace of mind that you will actually have a passport before you travel.
Good luck