I asked this very question at BA T3 Club check-in recently and was told that I could not use Fast Track. I looked very carefully at the entrance for a sign, because this elusive mythical item had been mentioned on FlyerTalk before, but to no avail. To the two of you who claim there is a sign (but disagree about what it says) could you tell me precisely where it is? I asked at the entrance and, of course, the goon had no idea - he just grunted. I would have had to enter the queue for the desk to find out.

I have used T3 Fast Track this year when travelling in CE (or, I think more precisely, IB Biz). It seemed to be of the usual BAA miss-the-point standard and take the same time as Slow Track; but unlike at T5 you can't see one from the other although a Fast Track user walks past the Slow Track exit on the way out so can get a glimpse of the queues.

P.S. Ah sorry, I missed this bit:
But that means you have to walk some way into the Fast Track section before you actually see the sign. (At least, I definitely could not see it from the entrance where the goons with the bags are.) By that point you've already decided that you're a Fast Track chap.