I had always been curious about adhesives in cling wrap. Google is my friend. Turns out the plastic itself has no cling properties; it’s an adhesive that is applied that creates the tack.
I don’t like the idea of adhesives in my food. It seems that polyisobutylene is a common adhesive, as this passage from a patent confirms.
Preferably the elastomeric polymer is a polymer containing at least partly units derived from isobutylene, preferably polyisobutylene homopolymer, VLDPE, or an ethylene-propylene rubber with suitable rheological properties and compatible to provide a low haze blend. Advantageously the elastomer is an olefin polymer of a higher olefin monomer from C4 to C13 and preferably polyisobutylene or polybutylene, said olefin polymer preferably having a Mv (Viscosity average molecular weight) 30 000 to 80 000. The elastomeric component should be used in amounts which do not give rise to compatibility problems; for this reason no more than 10, preferably 7%, is used. When polyisobutylene is used a PIB having an Mv of less than 30 000 will not impart sufficient strength and elasticity. Rather it may exude to the surface and provide an oily surface.
So seven percent or so is this polyisobutylene which is not very well bonded to the plastic itself. Doesn’t sound appetizing to me.