Changi Airport offers early check-in for most airlines; with Qantas you can check baggage 24 hours a day up to the day before. (SQ allows 48 hours).
BA have an "early check-in counter" open from 2pm-5pm daily (whatever that means).
http://www.changiairport.com/passeng...early-check-in
As for left luggage, Changi has left luggage facilities both Airside and Landside at each of terminals 1, 2 & 3.
http://www.changiairport.com/at-chan...ggage-services