Surely the pipeline should be:
0. Before anything 1 staff takes your money
1. Staff 2 checks licence requirements against provided evidence (checklist).
2. Staff 2 presses print (for licence + envelope)
3. Staff 2 signs licence
4. Staff 2 puts items in envelope
5. Staff 2 sticks on label
6. Staff 2 puts envelope in the trolley
7. Staff 3 takes trolley to postman waiting at the door to pick it all up
Single licence application should take a whole.... 10-15 minutes from start to finish (applications for ratings to be applied: ie night probably take less than 5minutes in all). Assuming that the average is 40 hours per week in most jobs (i think the CAA is different though); That would otherwise be 160 licences per week per person working. Hence if you 18 people working on applications alone that'd be: 2,880 licences per week. (if an NHS GP can find out what's wrong with you, give you advice, write in the notes, print & sign a prescription in 10minutes or less - I don't think its impossible!)
That means that they could clear the backlog in half a week!
OK, let's be fair - they only work 6 hours per day, out of the 18, 2 are on leave, 1 is ill, so only 15 are in the office, 2 are managers who oversee their colleagues and don't help in a time of need, 1 is a phone operator answering people who keep asking "where is my licence?", 1 person is in charge of taking the money and 1 person is the admin support staff (ie making tea / putting packages in the mail... etc...). Meaning you end up with only 10 people actually dealing with the paperwork. If it takes them 20 minutes for each application, that's 90 applications per week per staff. Or a total of 900 applications processed per week. In other words, clear the backlog + new arrivals in two weeks, and then only need to process less than 30 applications per week (or estimated 10 hours per week) just to make sure that they're clearing the backlog. Also means that they can work 2 days a week and still earn the same money and we don't have to wait for our licences!
I bet they process the licences on the day they arrive, and then put them on a pile "to be sent on stated date" and then the piles only get sent several weeks after they've been processed!