On the soft fabric or the waterproof type stuff? If the latter, then you could patch test a hidden bit of it with something like Dettol Mould and Mildew remover to see if it affects the fabric. If it's safe, then a couple of minutes with the chemicals, then a really, really good rinse and wash with detergent and a proper airing should sort it out. (My mum did the same with a buggy before.)
Hmm, A wash with some bleach in the water could sort it. Again, patch test. If not, I'd try the mildew remover. I have successfully used it on man-made fibres before, but you do run the risk of damaging the fabric.