It is possible for humans to ingest small particles of plastic which have been consumed by the animals we eat.
Currently, there is no evidence to say that microplastics in fish pose any risk to human health.
The toxins referred to in relation to our oceans have generally been in the environment for a long time. POPs (Persistent Organic Pollutants) are largely present from times when regulations on chemicals and fertilisers were not as strict as they are today. POPs are never present in the plastics created today (except for a specific flame retardant used in high-end aerospace applications) and sea creatures would be exposed to POPs already in the sea regardless of whether plastic is present.
Preliminary indications show that “microplastics play a minor role among the large variety of natural particles in delivering POPs to higher trophic levels”, as reported by (GESAMP Report 93, 2016).
A new global analysis of seafood found that fish populations throughout the world's oceans showed that POP levels have declined in the past 30 years.
So, when it comes to POPs, fish are safer to eat today than they were 30 years ago.