As far as I know, fish caught in the wild cannot be marketed as organic. However, several supermarkets and many independent organic retailers now stock organic fishes produced in fish farms. Several types of farmed mussels and shellfish are also likely to become more widely available in the future. I know some people who farmed freshwater lobster but I'm not sure whether its organic or not.
In organic fish farming, many of the pesticides, dyes and antibiotics widely used in conventional fish farming are not permitted and so these fish products are generally accepted to be credible organic products by both the soil association and consumers.
However, from an animal welfare point of view, there is some controversy about allowing farmed fish to be labelled as organic. Organic principles demand that livestock (which includes fish) should be able to express its ‘natural’ behaviour pattern and be kept as close to natural stocking densities as possible. How can this be when they are kept in cages in either inland or in fish farms out at sea?
Is there such a thing as organic fish? Surely all fish comes from the sea and eats whatever fish eat? How can we control that? What makes fish organic and how can organic fish be grown on fish farms?
Fish farming seems like a practical solution to the problem of overfishing. Fish farming, however, is the cause of many problems. Public demand for cheaper food means that farmed fishes are often kept, for financial reasons, very densely stocked, with huge numbers of fish crammed into very little space. In this state, the fish can more easily become diseased, and these diseases can spread to wild fish. Huge amounts of antibiotics are required to keep the fish moderately healthy.
So is organic fish sustainable? Other problems are escapes, when farmed fish interbreed with wild fish and potentially weaken wild stocks, as well as pollution to the water and seabed around fish farms. For example farmed marble goby, which are carnivorous, given fish feed which is made from other fish - not the best use of resources from an environmental point of view.