've read about some stuff called M.E.K. solvent cement, it's apparantly
sold primarily for sealing a plastic shower tray to the wall, but is also
used for plastic shower tray repairs,

MEK is a colourless clear solvent used for cleaning certain plastics
purposes. I doubt it will solve your problem. A sealant that contains
MEK might do it.

Firstly find out what plastic your shower is made of. Some are Styrene
some are Glass Re-inforced Polyester. Bit difficult to tell the
difference I will admit.

If it is GRP a car body repair kit will do the trick. You will have to
make the repair from the underside as it is not very pleasing to see
Glass Fibre Mat sticking up from the surface of the shower.

If it is styrene a model repair cement should do the trick but it is
not very strong. You will problably have to re-inforce it on the
underside of the shower with Glass Mat soaked with the repair cement.