Dave,
The problem with black mould is that it grows within the fabric - with natural fibres, within the fibre strands themselves.
The most effective treatment I have found is Ultrapac Renovate BUT results are most often dissapointing.
I have also had some sucess with peroxide bleaching boosted with ammonia as a final treatment but this is likely to cause undesired colour loss and posible fibre weakening.
Best left alone.
John.