Nixon peabody (law firm, US) song featured here once - a proper corker

No.  this did not happen.

"Everbody's a winner at Nixon pea-bo-dyyyy"

I'm now hearing "Uuuuuunilever!" in my head (to the tune of "Schadenfreude" from Avenue Q).

Good fooking god, I'd forgotten about this sort of shenanigans.

Nothing compares to the Deloitte rap ( appears to feature Laz heh)

Halliwells had a cracker, they then pulled it when the got widely ridiculed.

PwC had a song and a rap. 

What the actual...?  How did I miss this random shit? Lol!  Brilliant.

Rounding out the Big 4:

https://www.youtube.com/watch?v=MaIq9o1H1yo

Oh my sweet Jesus.  I honestly thought Wellers was taking the piss about a crap song.  But then I clicked on the link.

MY EARS