Smoke Grenade use in the Second World War

[Michael Dorosh]

Just rereading tracts of David Gordons' WEAPONS OF THE WWII TOMMY. He mentions the Ox and Bucks using smoke grenades to neutralize enemy bunkers on D-Day (they were WP so no doubt very effective for that purpose).

Were smoke grenades commonly used to provide smoke cover for troops in the field? I understand the 2-inch mortar was designed as the platoon's own "artillery" to fire HE, Smoke and Illumination. My understanding is that smoke grenades were used more for signalling (or, as the example above shows, as offensive weapons if WP) than for providing cover for troops.

Who was equipped with smoke grenades? I get the understanding German assault pioneers were equipped with same as they were used as specialists in city fighting. Were Canadian engineers ever tasked or equipped in this way?

Smoke grenade use is common today but I suspect- without knowning - it was different in the Second World War. What did the manuals of the day say with regards to smoke hand grenades?