When you say you bought tickets to the “London Opera”, do you mean the Royal Opera House in Covent Garden or the English National Opera at the Coliseum? Or elsewhere?
Anyway, I went to see an opera at Covent Garden earlier this year. Most women dressed up a little - a nice dress (but not an evening dress) and maybe a pretty scarf. I also saw women in leggings with smart tops, and some people who were just wearing jeans & normal clothes, clearly there after a day doing other stuff.
Anyway my point is: it’s not high society, and in fact the opera houses are trying to make it much less so. But you’ll probably feel more comfortable if you make an effort to dress fairly smartly but unless it’s a big gala night or premiere, you’ll see a huge range of clothes. I wore a simple smart day dress, black, but jazzed up with coloured tights, scarf and necklace.
It’s difficult to suggest transport without knowing where you’re coming from & to, but most people will use public transport - tube & buses are excellent, and you will see people looking pretty smart & dressy even on public transport. Otherwise, just flag down a black cab.
Leaving the venue, there’ll be lots of other people leaving at the same time and many of them will probably be heading straight for the tube or nearest bus stop.