I suggest using sheets of clear PVC:
It's non-adhesive, a lot more durable than the more common polypropylene sheets (like the perforated 'punched pockets'), but still supple. They mostly come in standard sizes, like in the image, pre-folded and stitched to accommodate certain book size standards (as an example, the page from which I sourced the image has A4, A4+, 165mm x 210mm, and 180mm x 240mm), but are available as sheets as well.
It's also sold under the name heavy-duty (protector) sheet, and it's easier to find complete sheets using that term. Searching for 'vinyl sheets', 'plastic roll film', 'clear soft PVC', or a combination of those keywords yields similarly useful results.
A slightly less sturdy variant, which is easier to find on rolls for this specific purpose, is called 'archival book jacket cover'.
For completion's sake, here's a WikiHow entry on wrapping books using these sheets.