Green’s Dictionary of Slang

Edna May n.

In phrases

on one’s Edna May [rhy. sl. = SE on one’s way]

(UK Und.) leaving, departing.

[UK]L. Lane Me and My Girl I iii: Bill: Nah gis me titfa and me turtle doves an’ I’ll be on me Edna May.

In exclamations

Edna (May)!

(UK Und.) a general excl. of dismissal: be off! go away!

[UK]D. Powis Signs of Crime 182: Edna (May)! On your way! (command to ‘clear off’).