Green’s Dictionary of Slang

drive-me-silly n.

[rhy. sl.]

(Aus.) a billy, the container used for boiling water.

[UK]E. Hill Territory 446: You take the drive-me-silly and go down to the bubble-and-squeak and get some mother-and-daughter, and I’ll light the Molly Maguire and we’ll have some Gypsy Lee.