Some sort of 2 part epoxy should hold up pretty well. Araldite is a common brand in the UK. For best results, try to remove the old glue so the bond is to the plastic itself, scuff both surfaces with sandpaper, then clean with something like alcohol to ensure the best bond. Allow to dry before applying epoxy. It's important to use the specified proportions of resin and hardener (usually 50:50) and that the two are well mixed. The epoxy should cure at room temperature or as specified, but once fully cured it will hold up under fairly extreme temperatures. It is also waterproof and resistant to most chemicals.
Be sure it is only applied to surfaces intended or materials disposable. It usually is impossible to remove once cured except by grinding away.
Besides epoxies, polyurethane based adhesives work well also. The two part versions are stronger but the more common one part formulas work quite well too and are more convenient to use. Such adhesives can be found in sizes anywhere from small craft quantities up to large tubes of construction adhesive by the case. Note that not all construction adhesives are polyurethane based.