They started arriving at Poldhu Cove on the Lizard on Sunday, and National Trust volunteers have been clearing them away as they are said to pose a risk to wildlife.
The bottles are sealed, but witnesses say some have leaked.
The National Trust said it believed a container had gone overboard from a ship, during the stormy weather.
The Maritime and Coastguard Agency said: "While it is fact that the MV Blue Ocean lost a container containing bottles of 'Vanish', there is no currently available evidence that the bottles washed up on the Cornish coast are from this container; all evidence is currently circumstantial."
It is thought the vessel lost the container near Land's End in May.
The BBC has contacted Vanish, but the company is yet to comment.
Other nearby coves including Gunwalloe, Polurrian, Church Cove and Marazion have also been affected, conservationists said.
Cornwall Wildlife Trust said it was "highly concerned" about the impact on "sensitive marine life".
Justin Whitehouse, from the National Trust, said: "The main worry is all that detergent going into our beautiful marine environment, but thankfully most are full.
"We think it's a container that has gone overboard from a container ship, during stormy seas."
Cornwall Council said the authority and partners, including the Maritime and Coastguard Agency and Natural England, would be monitoring beaches in the area.
It said: "The National Trust who own the beach at Poldhu have arranged for the bottles to be cleared away.
"In the meantime the public are advised to keep children and dogs at a safe distance from the bottles should any more be washed up.
"No attempt should be made to recover the bottles."
Thousands of bright pink plastic detergent bottles have washed up on beaches in Cornwall.