Buy some sodium hydroxide, aka caustic soda, on
Ebay (about £5 for a kilo of crystals if you look hard). Buy it in a plastic container, NOT a bag.
Fill a one litre kitchen measuring jug, either glass or plastic, three quarters full of warm water and gradually add some of the sodium hydroxide one large tablespoon at a time. As you do so, stir the mixture with a non-metallic spoon or stick. I just continue to add more until it looks like additional crystals will not dissolve. The mixture will get very hot and will fizz so wear some eye protection, gloves and old clothes. The solution will not take any prisoners.
Get the grating off the shower trap and feed a thin, rolled-up kitchen sponge mat into the trap to suck up as much excess water as possible. Repeat until you can't get any more water out. Then pour about a half of the lethal solution down the plug-hole and leave it for 45 minutes. Rinse, bail it out again with the sponge mat, and repeat. It'll work.
Don't spill any of the liquid on anything.