USe a little imagination!!

Up the close and down the stair,
But and ben with Auld Rapaire,
Stilly's bright, and Ted's the thief,
But Bunnhabain brings out the beef.


Now, sir Librarian, can you tell us in the ragamuffin's rhyme from the days of corpse-selling in Old London, what the the line:

Up the close and down the stair,
But and ben with Burke and Hare,

means in modern language? What words are "but" and "ben" herein?

A

(I know better than to expect anything but tatterdamalion non sequiturs for a response, but hope springs eternal and all that....)