I do it all the time- but it did take practice! I bought a cover but LO hated it- think she felt too smothered and can't blame her! I bought a couple of casual nursing tops from mothercare- they are brill and were not very expensive (also on a 3 for 2 offer). Well worth investing on what you'd save on formula! Also stretchy long vest tops under a loose top do well so my tummy stays covered, and the top helps cover baby so is discreet.
First time I did it in public was in Costa coffee- I was uncomfy on a high stool, it was very busy and I got flustered- LO definitely picked up on this and wouldn't latch properly. I did get stressed and upset- but don't give up! First find somewhere you're comfortable- at my local shopping centre I know debenhams cafe is baby friendly as they have bottle warmers and lots of mums in there- I choose a table where my back is to the room so no one can see. Lots of big shopping centres have specific nursing rooms which I found to be good. Also shops like boots, mothercare and John Lewis have feeding rooms. If I haven't been able to find anywhere I feel comfy I've gone back to the car to do it.
Last week I was shopping somewhere unfamiliar- couldn't find any nursing rooms, the cafés were all mad busy and I didn't know what to do! In the end, I sat in a bench in the middle of the shopping center (I was wearing one of my mothercare tops, and I'm so practised now I got her on discreetly and no one would have been able to see anything. I felt wary of others at first as many shoppers passed by, but most didn't even look at me- people were busy going about there own business! One woman noticed and smiled at me, and an elderly woman came over to ask the time, then told me I was doing a terrific job looking after my baby! Made me really happy and think I should do it more (now I'm confident and discreet) as it will help normalise it! Just practice at home, and don't start feeding until you feel comfy and calm. X