Apparently R.J. Reynolds has a division in England; British American Tobacco Co., which originated the brand in Merry Olde England, and then brought them to the States.
Going by the very strict pronunciation given on the ‘net, neither Pall Mall nor Pell Mell are correct. The correct pronunciation is Pal Mal. Pal, as in my pal Sal; and Mal to rhyme with it. And to think; I used to smoke ‘em occasionally before I quit, and never pronounced it correctly.
If you’re talking about the cigarette, Pal Mal is probably closest to correct, according to everything I’ve ever heard. But the street in London is not pronounced the same way, nor is the synonym for “headlong” or “chaotic.”