Only had one done in haste about 15 years ago, mine had a few days left, checked on phone and they said the airline might not let me fly as it would be expired if there was any flight delay on the way back. Headed down to Liverpool handed stuff in mid morning , car keys and mobile into tray etc, chatted up this female security guard which think might have helped. I was also dressed like I was on the beach which might have told them i needed it asap. Flight was 9pm ish so when I handed it in I said I needed it same day , they said "mid afternoon".
So I did some shopping for partner had a few pints visited Cavern Club , Liver Building etc. Went back about 1.30-2pm they said it had been ready ages. Dropped car off at long stay, bus to airport, we were drinking in bar pre flight at 6pm . I was well pissed when I got on plane.
Every time I done it by post it's been a 6-9 months before flight so never been in a rush so never took notice of posting time which i guess is the info you need. Know 6-7 people who also done a same day one family and friends so as Blueish Swede said "if you don;t mind scouse accents" do it that way if you want it in your hand . If not read the posts of people who have had more recent experiences by post.
Only posted this to let you know if you cock it up by mail , if you have transport you can always head to Dipper central and it won't take too long.