The Margiris and the Annie Hillina have reportedly been seen off the coast of Sussex, Hampshire and the Isle of Wight for the last few days.
Registered to Lithuania and owned by Dutch company Parlevliet van der Plas, the 6,200-tonne, 143-metre-long fishing vessel was once thought to be the second largest on Earth.
Watch stunning underwater Help Our Kelp campaign film, voiced by Sir David Attenborough, showcasing the vital role Sussex waters can play in fighting climate changeIt had been banned from fishing in Australian waters due to the impact it would have on fishing stocks. It pumps the fish directly on board from the nets and processes and packages them there.
The Annie Hillina is a German fishing vessel that weighs more than 2,000 tonnes.
Clive Fennell, from Parkside Avenue, Littlehampton, runs the Littlehampton Environment and Places Facebook page, and said he had seen the boats out to sea since Sunday.
The 58-year-old claimed that the Margiris could take the amount of fish in a day that two small trawlers could take in a year.
He said: "These little fishermen don't stand a chance. There will be nothing left.
"You can see the boats from Littlehampton in the distance, and you think they are miles away: but fish travel that distance. These are our local fish they are taking, and it is our local seals and dolphins getting caught in their nets."
According to the Marine Management Organisation (MMO), officers boarded and inspected the Margiris on Wednesday (October 2) and no infringements of fishing regulations were found.
The boat is fishing for horse mackerel and pilchards, the MMO said.
Methods of fishing are controlled by technical rules imposed by the EU to ensure fishing practices are carried out sustainably and with minimum impact to the environment, according to the MMO.
This comes amid turbulent times for fishermen, as the Sussex Inshore Fisheries Conservation Authority is consulting on by-laws which stop them fishing near the coast.
The Nearshore Trawling Byelaw 2019 forbids trawling between 1 and 4km (0.54 and 2.16 nautical miles) from the coast 'to protect nearshore essential fish habitats', and the Netting Permit Byelaw 2019 bans netting between 0.5 and 1.5km (0.27 and 0.81 nautical miles) from the coast 'to protect both migratory and juvenile fish stocks'.
Local inshore fishermen have spoken out about the laws, saying boats under 7 metres long which fish sustainably are being put in the same category as huge trawlers which damage the sea bed and the marine environment, and means their livelihood could suffer.
Clive said: "The irony is that they are pushing these local fishermen further out to sea, but these big trawlers are taking all the fish."
The consultation, which ends on October 10, allows the public to have their say before they are confirmed.