Barrels and nappies
More than 200 people roamed the beach on Monday, collecting items ranging from wooden barrels and car parts to nappies.
Under the merchant shipping act, salvage remains the property of the original owner and anyone finding washed-up goods must contact a government official - the "receiver of the wreck" - within 28 days.
The maritime and coastguard agency said people could be charged with theft if they failed to report the salvage they take from the beach.
Mark Clark, an MCA spokesman, said the scavengers were guilty of "crass greed".
He said: "They have quadrupled our task. People are lighting fires beside the containers, getting on top of them ripping stuff out, and not heeding our warnings.
"The MCA is deeply upset and angry because all the stuff which has been ripped out of the containers will be swept out to sea and have an environmental impact."
Heavy lifting equipment is to be moved down to the beach to begin removing the containers and other goods, and officers said the area would be dangerous and advised the public to stay away.
The British-flagged Napoli is listing at up to 25 degrees and has already lost waste oil and more than 100 of its 2,400 containers into the sea.
About 200 tonnes of oil have leaked but the MCA said this did not pose a major environmental threat.
Coastguards said salvage teams hoped to be able to start pumping out the remaining 3,000 tonnes of fuel oil from the ship's tanks, but experts warned this may take several days.
The vessel, built in 1991, was bound from Belgium to Portugal when it was holed.
Its 26 crew took to a lifeboat and were winched to safety by a helicopter.