With SQ lounge still closed, if you are on the later evening LHR-SIN flights (ours is 20:35), choose wisely.
If you arrive at the airport early you might score a shower at the UA lounge before they shut at 17:30, but when we arrived around 17:00, there was a queue.
As check in doesn't open until 16:35, as we discovered, there is not really a chance to check in, clear security, get into the UA lounge, and queue for a shower before they close.
So if you want a shower, stop in at the Plaza Premium lounge before you head across to the B gates and the UA lounge.
AC won't let you in as it is more than three hours ahead of departure, and they close at 17:30 anyway.