I don't think Rules has a dress code. Very few restaurants in London do now. I've been there a couple of times in the last year and I'm pretty certain I just turned up in whatever I was wearing, and on one occasion I was taking visitors who I'm equally certain were not dressed up. Certainly I would never think about it if I was planning on going there. (But then I take the view that if they threw me out I'd just go to one of at least 20 other good restaurants within 10 minutes' walk.)

The Royal Opera House is a lot less stuffy than it used to be. (And it's not Glyndebourne, which is different.) While there are a lot of "suits" in the stalls, many people go there straight from the office during the week. Smart trendy casual would not be "terribly out of place" there. In fact, if you are not in a suit somebody might get the impression that you know something about the art, rather than just spending the company's (or trust fund's) pound. But much will depend on how self-conscious a person you are.

If you are up in the nosebleed seats, though, definitely dress for comfort. Nobody will care. Those who turn up there in dinner suits (there are some, occasionally) are the ones who strangely out of place.