There are some useful Facebook Groups on this theme.
Some of the things I do:
- flannels for make-up removal is fine as I use different half of the flannel for each eye. But then, I don't wear much makeup.
- I take my own containers to the butchers & ask them not to use plastic bag. I also buy eggs at butchers - they have trays of eggs with empty egg cartons on the side, so I take my own egg cartons (yes they're just paper but there's a limit to paper's recyclability too so I always try to reuse paper things as well as plastic if there's still life left in them)
- I make good use of the plastic packet from inside cereal boxes. I cut them up into strips to layer food for freezing, and use the bags whole as freezer bags. Secure them with reusable plastic clips. For more delicate foods that go in the freezer, I reuse ice cream and other similar tubs, or Tupperware.
- Fruit & veg shopping: I try not to use any new bags - neither plastic nor paper. Anything that is single use is not great. Not only plastic. Even paper. Lots of energy & resources used to create & distribute paper bags. So always try to reuse something.
- Storing opened tins of cat food in the fridge - use empty pasta/pulses packet secured with reusable plastic clip.
- soap - I use a bar that is stored on a soap dish with ridges & a hole in it so gunk drains & soap stays dry.