I have been using the FastTrack at LHR T3 for sometime now regardless of cabin. In fact, on several occasions the checker directed me to the FastTrack when I was trying to go through the normal lanes.

But the FastTrack at T3 is not much of an advantage. It is a single lane vs. 5 lanes of normal processing. Sometimes, you end up waiting longer than the normal lanes, since there are quite a few business/first class pax. And you end up having to rejoin the regular lane crowd in the area to take off your shoes, where people tend to crowd up.