Have you tried "Dettox Anti-Bacterial Mould & Mildew Remover"? I have
found this product works exceptionally well. Just spray it on, and
within a few seconds you'll see it starting to work.
Be careful not to get any on your clothes, towels etc, because it'll
bleach them. The 'trigger spray' often leaks mind, but I understand
they have redesigned it now (?)
I second the above.
It's the ONLY product I have found that works on shower mats.