If you’re first off, the BA lounge is fine. But given the numbers wanting a shower, if you’re not first in the queue then QF is better. Don’t worry about being early for security, it’s right at the gate and they won’t close the flight while there are people still in the queue. Remember that liquids rules still apply, so if you keep an amenity kit put the bits in your standard toiletries bag, and if buying duty free in London remember to ask for a STEB.