Well heres what I found earlier.
Australian War Memorial2/33rd AustralianInfantry Battalion; QX61195 Private Henry Richard Maris, 2/33 Btn; using a rifle grenade launcher with EY (Edward Yule - inventor) discharger cup (these were ordinary .303 rifles no longer suitable for use as a rifle, but with the discharger cup fitted they were used as grenade launchers, copper wire wound around hand guards on barrel to prevent barrel rupturing when fired)
Sounds like the EY marking came before the decision to have EY marked rifles designated as Emergency Use Only.
EY just never sounded much like it was meant to stand for the word Emergency. The propensity of the Britishto string initials together such as "STEN" and "BREN" would seem to point to Edward Yule's Initials being the origin of the markings.
Of course it could have been Uncle Vinny who came up with the term "Emergency Youse" but I doubt it.