I fed DD till she was over 3, and living in London, I fed her on buses, the tube, in the middle of John Lewis, wherever.
I bought a load of tops from eBay from a company called Mamaway - I really liked their polonecks. There was a kind of vest bit and then the whole front was a flap that poppered down each side. You just unpoppered the appropriate side and latched the baby on - no boob and no tummy showing. Otherwise, vests under clothes and lots of cardigans - shirts with buttons are not a good choice.
Nursing bras were a total pita - impossible to do the clip things in a hurry. Instead I bought soft T-shirt bras and just folded them down under boob to feed. Also handy if there is the odd leak. I didn't find underwiring a problem at all.
Definitely practice in front of the mirror so you can see what you are doing and how to do it without flashing the world - and to do it fast before kiddo has screamed the place down. Until they get to the point of stopping for a good look-around it is possible to breast-feed without anyone seeing so much as a nipple. I'm a 34 DD, so not as if I haven't got much to potentially display.
Shawls etc were a complete nightmare and DD hated things over her head so I ditched them fast.
Once they're a bit older, you can even feed them in a sling. I had an Ellaroo Mei Tai, and I would undo the knot and move her down a bit to feed and then undo the knot and hoik her back up again afterward. Fed her many, many times while walking round the supermarket - not even my mother noticed.
Certainly in London most people are quite happy with public breastfeeding. I got lots of compliments from elderly ladies on buses for some reason, and even a couple of men saying it was a beautiful thing to see. Never had a single negative comment in 3 years.