Simon, I currently drive on Pirelli touring tires. It is time for new ones though. Car pulled with prior tires also, so I don't think that's the problem with mine.
I intend to do some front suspension work within a couple of weeks -- replace both tie rods (no play, but busted seals), replace drag link, install a idler repair kit, and realign (this time at the Mercedes dealer).
I'll keep you posted if I find the problem.