The most common and most likely answer to this crossword clue is the 8 plus 2 plus 3 plus 5 letter word NINETEEN TO THE DOZEN
I've seen this crossword clue in The Guardian
N
I
N
E
T
E
E
N
T
O
T
H
E
D
O
Z
E
N
Buddy explains!
The straight part
We know that "quickly, so to speak" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case quickly, so to speak = nineteen to the dozen.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.