Well, you could go to a packaging-free supermarket, many of which are listed
The most practical thing to do is try to shop from places like Lush who make it easy to buy unpackaged or paper-packaged goods, and who offers rewards to those who bring their plastic containers back to be refilled. Which begs the question, why would you want a potentially cancer-promoting material on your lips anyway? If you’re drinking in, you don’t need a lid. If you’re not, there are plenty of reusable coffee cups on sale made from glass or bamboo which are both attractive and better at keeping your drinks hot.
It’s a start and an opportunity to see just how much plastic we subconsciously consume every single day. Once you start noticing it, you’ll be horrified.