Fitting a new seat cover

I have a new seat cover kit from RGM which I wanted to fit this weekend.
When I stripped the old cover off, the seat foam was wrapped in a fairly thick plastic sheet, obviously to prevent the foam from absorbing rain water.
However, when I fit the new cover, there's several ugly marks appear due to the folds of the plastic sheet.
The cover is sewn, not welded, so presumably it will let water through.
When looking through the net for discussions on fitting new seat covers, I don't see any mention of wrapping the foam in plastic, but on the other hand, I don't want to have a wet bum every time the bike is out in the rain, so what do other people do here? Just put up with the marks, use a thin plastic bin liner or ???

Why not the plastic film for food.........very thin and supposed to be water proof ??

they call it cling film ............

Ah, good idea there. Time to raid the kitchen

Many thanks for that.

I have used cling film and it works, not only for water proofing but the slippyness helps when pulling the cover taut.

Make sure your seat base is up to snuff in all ways first. No rust no cracks no "bent out of shape'. Sort all that first.
As usual, make use of my inattention to such detail. :-(

I think the stretchable clear plastic film they use for waterproofing large parcels, pallet loads of freight etc would be better than domestic cling film. It's very tough and readily available in hardware stores.