I have a green plastic water butt which has split at the bottom
because I foolishly didn't put it on a proper level surface, and the
weight of the water has done the damage.

I've repaired my water butts. I used a waterproof silicone sealant that I
bought from a DIY store such as B&Q, Homebase etc. Just squirt it into the
gap, leave to dry for at least 24 hours. Repair the hole from both sides,
i.e. inside the butt and outside.

- h