Matt,
Among US suppliers, I would probably use either a beta-cyanoacrylate in gel form (a thicker "super glue" with longer working time, gap-filling ability, and capable of bonding leather, fabric, and wood in addition to the usual list of surfaces)
...or...
McNett's SeamGrip, a specialized adhesive that remains rubbery to some degree after curing and sticks like pine tar.
The choice would depend on the plastic. If it felt a little rubbery or waxy, I'd go with the SeamGrip.
I'm not sure this product is available in your locale, but I feel sure it would work if applied, then covered with waxed paper under a clamp or weight (bed post leg?) overnight. The waxed paper prevent any squishout from sticking to the clamp.
All the best,
Dan.