ECAM,
Ideally they want type rated people for the 777 (or the -400 for one or two). Having said that, I don't think they're getting the numbers they want so as you're ZFT qualified, I think you'd have a fair chance.
However, you'd probably be told on the day you start where you're going, and what it says at the top of your contract doesn't automatically mean that's where you'll end up. Whenever any of us who are there already bid for a new fleet, it isn't guaranteed that you're on your new type until you actually fly the aeroplane!! I'm not joking.
If you apply, you may well get the 777, there is a significant requirement. However, be prepared to be offered anything else. The -400 is pretty unlikely, although not to be ruled out entirely so expect the A320 as the alternative.
Also, decide how badly you want a command. It will not happen at BA for a loooooonnnnnnnnngggg time. By the company's own admission, it's 17+ years for shorthaul. Maybe worth making the point to them that if you're offered the A320, you'd rather stay put.
Caveat Emptor.