I am not a regular wearer of much make-up, but when my existing products do run out I shall be replacing them gradually with plastic-free refills from the award-winning Scotland-based Love the Planet and re-using my existing make-up packaging (or using my hoard of super-cute teeny-tiny jam jars).
Love the Planet's affordable vegan mineral make up range (face powder, concealer powder, blusher, eye shadow / brow definer / eyeliner, translucent finishing powder) is sent out in paper / cellulose film packaging (even the zip loc bit is made of starch not plastic!) for you to decant. When you open the papery package, do so in the (easily wiped) kitchen / bathroom over a sheet of paper (so any powder spillage can be saved and tipped into the jar too). I found that some powder was present above the starch zip-loc sealing strip- so opening it over a sheet of paper really is a must.
The 'neutral brown' eyeshadow / brow definer / eye liner powder comes in a 3g refill pouch (which fills about 1/8 of the miniature jam jar) - I will use this powder (with an existing make-up brush) instead of buying a new plastic-lidded eyebrow pencil.
If you are after bronzer powder then Cornwall's All Earth mineral make-up range (in cardboard refills) is worth a look.
Bain & Savon (based in Cumbria) make and sell a mascara liquid in a 15ml glass bottle with a metal screw cap lid. No brush is included, to encourage the re-use of your previous mascara wand (washed and dried regularly of course to ensure good eye hygiene). To me this looks like a mascara-spilling-accident waiting to happen. I am hoping that they will bring out a shallower-wider glass jar of mascara to make application easier (as you just want to glance your existing wand over the top of the product). If their packaging doesn't change then I will decant the mascara liquid into a shallow-with-a-wider-neck glass jar myself.
So choose wisely when you next buy make-up or perfume, as even these (traditionally overpackaged) luxuries can be plastic free - hurrah!