The Cockney accent is pretty much extinct at this point. Also, Grade needs to shout all the time to keep it up because having inflections in the voice would cause the accent to falter.
Grade doesn't speak with a Cockney accent. He speaks with an exaggerated Midlands accent, probably Leicester if I had to guess.
I watched some of his videos when they got upvoted to Reddit's front page and thought they were okay, though very "what's the deal with airplane food, huh?" style humor. The backlash was inevitable as it always is when Reddit really likes someone, but I wouldn't have guessed it'd happen this suddenly and this hard.