Coastguard officials hope to begin pumping 3,500 tonnes of oil from the stricken ship MSC Napoli to prevent more fuel leaking into the sea.
Up to 200 tonnes of oil from the engine room, mixed with water, has leaked from the cargo vessel, which is beached off the Devon coast.
But officials said the fuel contained in the ship's tanks, which have not been punctured, was their main concern.
The operation to remove the heavy fuel oil could last up to a week.
Paul Coley, of the Maritime and Coastguard Agency, said the fuel had to be heated before it could be off-loaded to a waiting vessel.
That process had been delayed but was due to get under way within the next 24 hours, Mr Coley said on Monday.
"There have been a few technical difficulties but we're hoping to start pumping later today or tomorrow," he said.
After the fuel oil has been transferred to another vessel, two cranes will be used to remove the containers from the Napoli.
A sheen of oil eight kilometres (five miles) long had been created on the sea surface after the engine room flooded, he said.
That oil was difficult to recover because it was so thin but Mr Coley added there were "no significant" reports of oil coming ashore.
The ship suffered structural damage during Thursday's storms and was deliberately beached off Branscombe to stop it sinking in deep water.
The ship has lost some 200 containers overboard, including two holding "dangerous but low-risk" goods.
Despite a warning to stay away from the containers, dozens of people reportedly spent the night "salvaging" thousands of pounds worth of goods on the shoreline.
The 62,000 tonne vessel was carrying 2,323 containers, 158 of which are classed as having potentially hazardous contents.
Of the 200 that have gone overboard, one contained battery acid and perfumes, and one small gas bottles for car airbags.
WHY IS THE AREA SO SPECIAL?
It's part of Britain's first natural World Heritage Site
The site covers 95 miles of coast from East Devon to Dorset
185 million years of the Earth's history are recorded in the rocks
It's known as the Jurassic Coast after the best-known geological period found within it
It was declared a World Heritage Site in December 2001 as 'an outstanding example of the major stages of the Earth's history'
Others housed a variety of goods including BMW motorbikes and car parts.
Not all of the containers have been found and some have broken up. Some may have sunk while others could be far out to sea.
Forms handed out
Police said they had drafted in extra officers as people searched the shore by torchlight for goods overnight.
Under the Merchant Shipping Act 1995 it is an offence for people to remove items from a wreck if they conceal or keep possession of cargo and refuse to surrender it, police said.
This photo of an oil covered bird was sent by Gareth Hughes
Officers handed forms to those searching the coast on which they must declare what items they have taken.
The ship was being towed to Portland Harbour in Dorset for a salvage operation, but on Friday coastguards decided to beach it because of its structural damage - a fracture on both sides.
An eight-person salvage team is on board, and a team of divers is being flown in to join them.
Environmental damage is so far said to be minimal. Three oil-covered birds have been found.
Residents in nearby Sidmouth have spoken of the concern about the leak.
One man told the BBC: "It's a real worry that we could get pollution and there's a lot of wildlife lives on these shores, and certain rare sea birds."
Julian Wardlaw, of the Environment Agency, said: "We have an extremely sensitive bit of coastline; we are dealing with a World Heritage Site and we are working to make sure that damage is minimised."
Meanwhile, it has emerged that the ship previously ran aground off Singapore in 2001.
It was previously named CMA-CGM Normandie and ran aground in the Strait of Malacca in 2001.
The ship subsequently had to undergo "major repairs" in Vietnam, according to Tore Hoifodt, senior vice president at DNV, which classes and inspects cargo ships.
People who may find a washed-up container are being asked to stay well clear and report it to Portland Coastguard on 01305 760439.
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