I've been making these wet wipe covers out of oilcloth, and I thought I'd share with you.
You need a rectangle of oilcloth 26cm by 40cm.
(I think some sturdy canvas type material might work too, normal cotton would be too floppy.)
Turn over the 2 shorter edges to make a hem each end of approximately 1 cm.
The oilcloth won't slip through the machine so you need to pin a layer of tissue paper over where you need to sew.
Sew the hems and rip the tissue off.
Next wrap your rectangle around a full pack of wipes.
There should be an overlap of about 2 cm. Pin each side.
Take the wipes out and pin the sides in place, making the opening central.
(Your cover should be inside out.)
Sew the sides up and tidy the loose threads.
Turn the right way out and it's done!
(Edited to add; if you cut a rectangle 20cm x 16cm, follow the same method and you will make a little pouch the right size for a pack of disposable tissues.)