I have the same problem with using QF (Emerald) status on BA. The boarding pass shows Group 1, but doesn't show Fast Track. If I print a boarding pass it will show Emerald, but if I use a mobile boarding pass it doesn't.
At Heathrow it has never caused any problems for Fast Track (or lounges), but at some other airports it has. I've not tried using my QF status at Gatwick, so unfortunately I haven't any personal experience of there. When turned away from Fast Track at another airport I was told in the BA lounge that security should have recognised that Group 1 is eligible for Fast Track. As Gatwick has a lot of BA flights I would expect security staff there to know that, so would hope you wouldn't encounter any problems there.
I used to get a "premium line" sticker when boarding pass failed to include "fast track" - e.g. flying Iberia Express as OWE.