Actually, just went to the Royal Opera two weeks ago and ate at Rules after.
Definitely no dress code at Rules (what you described would be fine).
Seriously, I'd wear a tie at the Opera if you're in the stalls or a box. I wasn't sure beforehand and was very glad I wore a tie(and I'm always very casusally dressed when flying first class).
[This message has been edited by jtrader (edited 02-24-2003).]