"Cling film" is generically called "plastic wrap" in the 'States. The most familiar brand is "Saran wrap."
Another advantage of waxed paper over cling film / plastic wrap: It doesn't try to contract or wrinkle once it is laid down. Sometimes I reinforce the corners with a spot of clear tape, so the points where I tack it to the board are less liable to tear.
The Arrow plans below are covered with waxed paper:
You can see that it is a little translucent over the picture on top left; it isn't tacked down quite as flat there.
I'm really keen to start on the Arrow, but I'm committed to finishing and submitting a writing project first. The desire to start a new build is helping me stick to my writing and get it done!