BA currently use Zone G at T3. There is no First check-in area, as there are no flights with First from T3 at the moment (shorthaul only from T3). There are Club Europe desks on the left hand side of Zone G, opposite the Euro Traveller desks.
Originally Posted by
Strawb
There may be a Goon manning entry to priority check-in who will direct you to use a machine. Ignore.
There is no 'entrance' to priority check-in at T3, so I'm not sure what you mean.