Many years ago I heard the following on ?Radio4?.....
During WW2 RAF W/T operators did morse code training in Liverpool, in rooms above a branch of Burton the tailor. Each day of the course trainees had to be faster at sending and receiving than the previous day, if not they were chopped from the course. Then they went down the stairs "for a burton".
Not saying it's the derivation.... but it is a nice story.
TP